diff --git a/ixmp4/core/optimization/data.py b/ixmp4/core/optimization/data.py
index 1bf5a295..3d085e78 100644
--- a/ixmp4/core/optimization/data.py
+++ b/ixmp4/core/optimization/data.py
@@ -2,6 +2,7 @@
 
 from ..base import BaseFacade
 from .indexset import IndexSetRepository
+from .parameter import ParameterRepository
 from .scalar import ScalarRepository
 from .table import TableRepository
 
@@ -11,11 +12,13 @@ class OptimizationData(BaseFacade):
     IndexSet, Table, Variable, etc."""
 
     indexsets: IndexSetRepository
+    parameters: ParameterRepository
     scalars: ScalarRepository
     tables: TableRepository
 
     def __init__(self, *args, run: Run, **kwargs) -> None:
         super().__init__(*args, **kwargs)
         self.indexsets = IndexSetRepository(_backend=self.backend, _run=run)
+        self.parameters = ParameterRepository(_backend=self.backend, _run=run)
         self.scalars = ScalarRepository(_backend=self.backend, _run=run)
         self.tables = TableRepository(_backend=self.backend, _run=run)
diff --git a/ixmp4/core/optimization/parameter.py b/ixmp4/core/optimization/parameter.py
index abd4c0cf..6612be41 100644
--- a/ixmp4/core/optimization/parameter.py
+++ b/ixmp4/core/optimization/parameter.py
@@ -34,12 +34,20 @@ def data(self) -> dict[str, Any]:
     def add(self, data: dict[str, Any] | pd.DataFrame) -> None:
         """Adds data to an existing Parameter."""
         self.backend.optimization.parameters.add_data(
-            table_id=self._model.id, data=data
+            parameter_id=self._model.id, data=data
         )
         self._model.data = self.backend.optimization.parameters.get(
             run_id=self._model.run__id, name=self._model.name
         ).data
 
+    @property
+    def values(self) -> list:
+        return self._model.data.get("values", [])
+
+    @property
+    def units(self) -> list:
+        return self._model.data.get("units", [])
+
     @property
     def constrained_to_indexsets(self) -> list[str]:
         return [column.indexset.name for column in self._model.columns]
diff --git a/ixmp4/data/abstract/optimization/column.py b/ixmp4/data/abstract/optimization/column.py
index 856fc116..029d2361 100644
--- a/ixmp4/data/abstract/optimization/column.py
+++ b/ixmp4/data/abstract/optimization/column.py
@@ -14,8 +14,10 @@ class Column(base.BaseModel, Protocol):
     """Unique name of the Column."""
     dtype: types.String
     """Type of the Column's data."""
-    table__id: types.Integer
+    table__id: types.Mapped[int | None]
     """Foreign unique integer id of a Table."""
+    parameter__id: types.Mapped[int | None]
+    """Foreign unique integer id of a Parameter."""
     indexset: types.Mapped[IndexSet]
     """Associated IndexSet."""
     constrained_to_indexset: types.Integer
diff --git a/ixmp4/data/abstract/optimization/parameter.py b/ixmp4/data/abstract/optimization/parameter.py
index 86e8eda3..01e1cacc 100644
--- a/ixmp4/data/abstract/optimization/parameter.py
+++ b/ixmp4/data/abstract/optimization/parameter.py
@@ -170,7 +170,7 @@ def tabulate(self, *, name: str | None = None, **kwargs) -> pd.DataFrame:
 
     # TODO Once present, state how to check which IndexSets are linked and which values
     # they permit
-    def add_data(self, table_id: int, data: dict[str, Any] | pd.DataFrame) -> None:
+    def add_data(self, parameter_id: int, data: dict[str, Any] | pd.DataFrame) -> None:
         r"""Adds data to a Parameter.
 
         The data will be validated with the linked constrained
@@ -183,7 +183,7 @@ def add_data(self, table_id: int, data: dict[str, Any] | pd.DataFrame) -> None:
 
         Parameters
         ----------
-        table_id : int
+        parameter_id : int
             The id of the :class:`ixmp4.data.abstract.optimization.Parameter`.
         data : dict[str, Any] | pandas.DataFrame
             The data to be added.
diff --git a/ixmp4/data/api/optimization/column.py b/ixmp4/data/api/optimization/column.py
index 229bb5cf..582c2314 100644
--- a/ixmp4/data/api/optimization/column.py
+++ b/ixmp4/data/api/optimization/column.py
@@ -14,7 +14,8 @@ class Column(base.BaseModel):
     id: int
     name: str
     dtype: str
-    table__id: int
+    table__id: int | None
+    parameter__id: int | None
     indexset: IndexSet
     constrained_to_indexset: int
     unique: bool
diff --git a/ixmp4/data/api/optimization/parameter.py b/ixmp4/data/api/optimization/parameter.py
index 0c272e78..32b21cc1 100644
--- a/ixmp4/data/api/optimization/parameter.py
+++ b/ixmp4/data/api/optimization/parameter.py
@@ -57,13 +57,13 @@ def create(
             column_names=column_names,
         )
 
-    def add_data(self, table_id: int, data: dict[str, Any] | pd.DataFrame) -> None:
+    def add_data(self, parameter_id: int, data: dict[str, Any] | pd.DataFrame) -> None:
         if isinstance(data, pd.DataFrame):
             # data will always contains str, not only Hashable
             data: dict[str, Any] = data.to_dict(orient="list")  # type: ignore
         kwargs = {"data": data}
         self._request(
-            method="PATCH", path=self.prefix + str(table_id) + "/data/", json=kwargs
+            method="PATCH", path=self.prefix + str(parameter_id) + "/data/", json=kwargs
         )
 
     def get(self, run_id: int, name: str) -> Parameter:
diff --git a/ixmp4/data/db/iamc/base.py b/ixmp4/data/db/iamc/base.py
index af057f86..1d8b80b9 100644
--- a/ixmp4/data/db/iamc/base.py
+++ b/ixmp4/data/db/iamc/base.py
@@ -7,7 +7,6 @@
     Deleter,
     Enumerator,
     Lister,
-    NameMixin,
     Retriever,
     Selecter,
     Tabulator,
diff --git a/ixmp4/data/db/optimization/base.py b/ixmp4/data/db/optimization/base.py
index 2ef34ec6..8dfe5ac1 100644
--- a/ixmp4/data/db/optimization/base.py
+++ b/ixmp4/data/db/optimization/base.py
@@ -8,18 +8,14 @@
     Deleter,
     Enumerator,
     Lister,
-    OptimizationDataMixin,
-    OptimizationNameMixin,
     Retriever,
-    RunIDMixin,
     Selecter,
     Tabulator,
     TimestampMixin,
-    UniqueNameRunIDMixin,
 )
 
 
-class BaseModel(RootBaseModel, OptimizationNameMixin, TimestampMixin):
+class BaseModel(RootBaseModel, TimestampMixin):
     __abstract__ = True
     table_prefix = "optimization_"
 
diff --git a/ixmp4/data/db/optimization/column/model.py b/ixmp4/data/db/optimization/column/model.py
index 04002b5e..d1551013 100644
--- a/ixmp4/data/db/optimization/column/model.py
+++ b/ixmp4/data/db/optimization/column/model.py
@@ -1,7 +1,5 @@
 from typing import ClassVar
 
-from sqlalchemy import UniqueConstraint
-
 from ixmp4 import db
 from ixmp4.data import types
 from ixmp4.data.abstract import optimization as abstract
@@ -34,4 +32,4 @@ class Column(base.BaseModel):
     # Currently not in use:
     unique: types.Boolean = db.Column(db.Boolean, default=True)
 
-    __table_args__ = (UniqueConstraint("name", "table__id", "parameter__id"),)
+    __table_args__ = (db.UniqueConstraint("name", "table__id"),)
diff --git a/ixmp4/data/db/optimization/indexset/model.py b/ixmp4/data/db/optimization/indexset/model.py
index 9e0f5a19..e772f6aa 100644
--- a/ixmp4/data/db/optimization/indexset/model.py
+++ b/ixmp4/data/db/optimization/indexset/model.py
@@ -9,7 +9,7 @@
 from .. import base
 
 
-class IndexSet(base.BaseModel, base.UniqueNameRunIDMixin):
+class IndexSet(base.BaseModel):
     NotFound: ClassVar = abstract.IndexSet.NotFound
     NotUnique: ClassVar = abstract.IndexSet.NotUnique
     DeletionPrevented: ClassVar = abstract.IndexSet.DeletionPrevented
diff --git a/ixmp4/data/db/optimization/parameter/model.py b/ixmp4/data/db/optimization/parameter/model.py
index 6bdcf67a..3199675d 100644
--- a/ixmp4/data/db/optimization/parameter/model.py
+++ b/ixmp4/data/db/optimization/parameter/model.py
@@ -1,16 +1,16 @@
+import copy
 from typing import Any, ClassVar
 
-import pandas as pd
 from sqlalchemy.orm import validates
 
 from ixmp4 import db
 from ixmp4.data import types
 from ixmp4.data.abstract import optimization as abstract
 
-from .. import Column, base
+from .. import Column, base, utils
 
 
-class Parameter(base.BaseModel, base.OptimizationDataMixin, base.UniqueNameRunIDMixin):
+class Parameter(base.BaseModel):
     # NOTE: These might be mixin-able, but would require some abstraction
     NotFound: ClassVar = abstract.Parameter.NotFound
     NotUnique: ClassVar = abstract.Parameter.NotUnique
@@ -18,13 +18,20 @@ class Parameter(base.BaseModel, base.OptimizationDataMixin, base.UniqueNameRunID
 
     # constrained_to_indexsets: ClassVar[list[str] | None] = None
 
-    # TODO Same as in table/model.py
-    columns: types.Mapped[list["Column"]] = db.relationship()  # type: ignore
+    run__id: types.RunId
+    columns: types.Mapped[list["Column"]] = db.relationship()
+    data: types.JsonDict = db.Column(db.JsonType, nullable=False, default={})
 
     @validates("data")
     def validate_data(self, key, data: dict[str, Any]):
-        data_frame: pd.DataFrame = pd.DataFrame.from_dict(data)
-        data_frame_to_validate = data_frame.drop(columns=["values", "units"])
-
-        self._validate_data(data_frame=data_frame_to_validate, data=data)
-        return data_frame.to_dict(orient="list")
+        data_to_validate = copy.deepcopy(data)
+        del data_to_validate["values"]
+        del data_to_validate["units"]
+        _ = utils.validate_data(
+            key=key,
+            data=data_to_validate,
+            columns=self.columns,
+        )
+        return data
+
+    __table_args__ = (db.UniqueConstraint("name", "run__id"),)
diff --git a/ixmp4/data/db/optimization/parameter/repository.py b/ixmp4/data/db/optimization/parameter/repository.py
index 48a3c1f1..735194fe 100644
--- a/ixmp4/data/db/optimization/parameter/repository.py
+++ b/ixmp4/data/db/optimization/parameter/repository.py
@@ -74,7 +74,8 @@ def add(
         run_id: int,
         name: str,
     ) -> Parameter:
-        parameter = Parameter(name=name, run__id=run_id, **self.get_creation_info())
+        parameter = Parameter(name=name, run__id=run_id)
+        parameter.set_creation_info(auth_context=self.backend.auth_context)
         self.session.add(parameter)
 
         return parameter
@@ -154,7 +155,7 @@ def add_data(self, parameter_id: int, data: dict[str, Any] | pd.DataFrame) -> No
         missing_columns = set(["values", "units"]) - set(data.columns)
         assert (
             not missing_columns
-        ), f"Parameter.data must include the column(s): {' ,'.join(missing_columns)}!"
+        ), f"Parameter.data must include the column(s): {', '.join(missing_columns)}!"
 
         # Can use a set for now, need full column if we care about order
         for unit_name in set(data["units"]):
diff --git a/poetry.lock b/poetry.lock
index 1c615801..5332c684 100644
--- a/poetry.lock
+++ b/poetry.lock
@@ -508,6 +508,26 @@ files = [
     {file = "distlib-0.3.8.tar.gz", hash = "sha256:1530ea13e350031b6312d8580ddb6b27a104275a31106523b8f123787f494f64"},
 ]
 
+[[package]]
+name = "dnspython"
+version = "2.6.1"
+description = "DNS toolkit"
+optional = false
+python-versions = ">=3.8"
+files = [
+    {file = "dnspython-2.6.1-py3-none-any.whl", hash = "sha256:5ef3b9680161f6fa89daf8ad451b5f1a33b18ae8a1c6778cdf4b43f08c0a6e50"},
+    {file = "dnspython-2.6.1.tar.gz", hash = "sha256:e8f0f9c23a7b7cb99ded64e6c3a6f3e701d78f50c55e002b839dea7225cff7cc"},
+]
+
+[package.extras]
+dev = ["black (>=23.1.0)", "coverage (>=7.0)", "flake8 (>=7)", "mypy (>=1.8)", "pylint (>=3)", "pytest (>=7.4)", "pytest-cov (>=4.1.0)", "sphinx (>=7.2.0)", "twine (>=4.0.0)", "wheel (>=0.42.0)"]
+dnssec = ["cryptography (>=41)"]
+doh = ["h2 (>=4.1.0)", "httpcore (>=1.0.0)", "httpx (>=0.26.0)"]
+doq = ["aioquic (>=0.9.25)"]
+idna = ["idna (>=3.6)"]
+trio = ["trio (>=0.23)"]
+wmi = ["wmi (>=1.5.1)"]
+
 [[package]]
 name = "docutils"
 version = "0.20.1"
@@ -519,6 +539,21 @@ files = [
     {file = "docutils-0.20.1.tar.gz", hash = "sha256:f08a4e276c3a1583a86dce3e34aba3fe04d02bba2dd51ed16106244e8a923e3b"},
 ]
 
+[[package]]
+name = "email-validator"
+version = "2.1.1"
+description = "A robust email address syntax and deliverability validation library."
+optional = false
+python-versions = ">=3.8"
+files = [
+    {file = "email_validator-2.1.1-py3-none-any.whl", hash = "sha256:97d882d174e2a65732fb43bfce81a3a834cbc1bde8bf419e30ef5ea976370a05"},
+    {file = "email_validator-2.1.1.tar.gz", hash = "sha256:200a70680ba08904be6d1eef729205cc0d687634399a5924d842533efb824b84"},
+]
+
+[package.dependencies]
+dnspython = ">=2.0.0"
+idna = ">=2.0.0"
+
 [[package]]
 name = "et-xmlfile"
 version = "1.1.0"
@@ -560,22 +595,46 @@ tests = ["asttokens (>=2.1.0)", "coverage", "coverage-enable-subprocess", "ipyth
 
 [[package]]
 name = "fastapi"
-version = "0.110.1"
+version = "0.111.0"
 description = "FastAPI framework, high performance, easy to learn, fast to code, ready for production"
 optional = false
 python-versions = ">=3.8"
 files = [
-    {file = "fastapi-0.110.1-py3-none-any.whl", hash = "sha256:5df913203c482f820d31f48e635e022f8cbfe7350e4830ef05a3163925b1addc"},
-    {file = "fastapi-0.110.1.tar.gz", hash = "sha256:6feac43ec359dfe4f45b2c18ec8c94edb8dc2dfc461d417d9e626590c071baad"},
+    {file = "fastapi-0.111.0-py3-none-any.whl", hash = "sha256:97ecbf994be0bcbdadedf88c3150252bed7b2087075ac99735403b1b76cc8fc0"},
+    {file = "fastapi-0.111.0.tar.gz", hash = "sha256:b9db9dd147c91cb8b769f7183535773d8741dd46f9dc6676cd82eab510228cd7"},
 ]
 
 [package.dependencies]
+email_validator = ">=2.0.0"
+fastapi-cli = ">=0.0.2"
+httpx = ">=0.23.0"
+jinja2 = ">=2.11.2"
+orjson = ">=3.2.1"
 pydantic = ">=1.7.4,<1.8 || >1.8,<1.8.1 || >1.8.1,<2.0.0 || >2.0.0,<2.0.1 || >2.0.1,<2.1.0 || >2.1.0,<3.0.0"
+python-multipart = ">=0.0.7"
 starlette = ">=0.37.2,<0.38.0"
 typing-extensions = ">=4.8.0"
+ujson = ">=4.0.1,<4.0.2 || >4.0.2,<4.1.0 || >4.1.0,<4.2.0 || >4.2.0,<4.3.0 || >4.3.0,<5.0.0 || >5.0.0,<5.1.0 || >5.1.0"
+uvicorn = {version = ">=0.12.0", extras = ["standard"]}
 
 [package.extras]
-all = ["email-validator (>=2.0.0)", "httpx (>=0.23.0)", "itsdangerous (>=1.1.0)", "jinja2 (>=2.11.2)", "orjson (>=3.2.1)", "pydantic-extra-types (>=2.0.0)", "pydantic-settings (>=2.0.0)", "python-multipart (>=0.0.7)", "pyyaml (>=5.3.1)", "ujson (>=4.0.1,!=4.0.2,!=4.1.0,!=4.2.0,!=4.3.0,!=5.0.0,!=5.1.0)", "uvicorn[standard] (>=0.12.0)"]
+all = ["email_validator (>=2.0.0)", "httpx (>=0.23.0)", "itsdangerous (>=1.1.0)", "jinja2 (>=2.11.2)", "orjson (>=3.2.1)", "pydantic-extra-types (>=2.0.0)", "pydantic-settings (>=2.0.0)", "python-multipart (>=0.0.7)", "pyyaml (>=5.3.1)", "ujson (>=4.0.1,!=4.0.2,!=4.1.0,!=4.2.0,!=4.3.0,!=5.0.0,!=5.1.0)", "uvicorn[standard] (>=0.12.0)"]
+
+[[package]]
+name = "fastapi-cli"
+version = "0.0.2"
+description = "Run and manage FastAPI apps from the command line with FastAPI CLI. 🚀"
+optional = false
+python-versions = ">=3.8"
+files = [
+    {file = "fastapi_cli-0.0.2-py3-none-any.whl", hash = "sha256:d7a8ec89fd52ad16c52de9fe7299e4b22c7a32e1bf28aa886e5517e4927423dd"},
+    {file = "fastapi_cli-0.0.2.tar.gz", hash = "sha256:589565ba758432632eadcf7b950e0ec76bb283b549784d9df17f261a8a9de476"},
+]
+
+[package.dependencies]
+fastapi = "*"
+typer = ">=0.12.3"
+uvicorn = {version = ">=0.29.0", extras = ["standard"]}
 
 [[package]]
 name = "filelock"
@@ -1368,6 +1427,61 @@ files = [
 [package.dependencies]
 et-xmlfile = "*"
 
+[[package]]
+name = "orjson"
+version = "3.10.3"
+description = "Fast, correct Python JSON library supporting dataclasses, datetimes, and numpy"
+optional = false
+python-versions = ">=3.8"
+files = [
+    {file = "orjson-3.10.3-cp310-cp310-macosx_10_15_x86_64.macosx_11_0_arm64.macosx_10_15_universal2.whl", hash = "sha256:9fb6c3f9f5490a3eb4ddd46fc1b6eadb0d6fc16fb3f07320149c3286a1409dd8"},
+    {file = "orjson-3.10.3-cp310-cp310-manylinux_2_17_aarch64.manylinux2014_aarch64.whl", hash = "sha256:252124b198662eee80428f1af8c63f7ff077c88723fe206a25df8dc57a57b1fa"},
+    {file = "orjson-3.10.3-cp310-cp310-manylinux_2_17_ppc64le.manylinux2014_ppc64le.whl", hash = "sha256:9f3e87733823089a338ef9bbf363ef4de45e5c599a9bf50a7a9b82e86d0228da"},
+    {file = "orjson-3.10.3-cp310-cp310-manylinux_2_17_s390x.manylinux2014_s390x.whl", hash = "sha256:c8334c0d87103bb9fbbe59b78129f1f40d1d1e8355bbed2ca71853af15fa4ed3"},
+    {file = "orjson-3.10.3-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl", hash = "sha256:1952c03439e4dce23482ac846e7961f9d4ec62086eb98ae76d97bd41d72644d7"},
+    {file = "orjson-3.10.3-cp310-cp310-musllinux_1_2_aarch64.whl", hash = "sha256:c0403ed9c706dcd2809f1600ed18f4aae50be263bd7112e54b50e2c2bc3ebd6d"},
+    {file = "orjson-3.10.3-cp310-cp310-musllinux_1_2_x86_64.whl", hash = "sha256:382e52aa4270a037d41f325e7d1dfa395b7de0c367800b6f337d8157367bf3a7"},
+    {file = "orjson-3.10.3-cp310-none-win32.whl", hash = "sha256:be2aab54313752c04f2cbaab4515291ef5af8c2256ce22abc007f89f42f49109"},
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 [package.dependencies]
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-    {version = ">=1.23.2,<2", markers = "python_version == \"3.11\""},
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+    {version = ">=1.23.2", markers = "python_version == \"3.11\""},
+    {version = ">=1.26.0", markers = "python_version >= \"3.12\""},
 ]
 python-dateutil = ">=2.8.2"
 pytz = ">=2020.1"
@@ -1469,13 +1583,13 @@ types-pytz = ">=2022.1.1"
 
 [[package]]
 name = "pandera"
-version = "0.18.3"
+version = "0.19.0"
 description = "A light-weight and flexible data validation and testing tool for statistical data objects."
 optional = false
 python-versions = ">=3.7"
 files = [
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 [package.dependencies]
@@ -1484,21 +1598,22 @@ numpy = ">=1.19.0"
 packaging = ">=20.0"
 pandas = ">=1.2.0"
 pydantic = "*"
-typeguard = ">=3.0.2"
+typeguard = "*"
 typing-inspect = ">=0.6.0"
 wrapt = "*"
 
 [package.extras]
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-dask = ["dask"]
+all = ["black", "dask[dataframe]", "fastapi", "frictionless (<=4.40.8)", "geopandas", "hypothesis (>=6.92.7)", "modin", "pandas-stubs", "polars (>=0.20.0)", "pyspark (>=3.2.0)", "pyyaml (>=5.1)", "ray", "scipy", "shapely"]
+dask = ["dask[dataframe]"]
 fastapi = ["fastapi"]
 geopandas = ["geopandas", "shapely"]
 hypotheses = ["scipy"]
 io = ["black", "frictionless (<=4.40.8)", "pyyaml (>=5.1)"]
-modin = ["dask", "modin", "ray"]
-modin-dask = ["dask", "modin"]
+modin = ["dask[dataframe]", "modin", "ray"]
+modin-dask = ["dask[dataframe]", "modin"]
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 mypy = ["pandas-stubs"]
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 pyspark = ["pyspark (>=3.2.0)"]
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@@ -1559,13 +1674,13 @@ test = ["appdirs (==1.4.4)", "covdefaults (>=2.3)", "pytest (>=7.4.3)", "pytest-
 
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 name = "pluggy"
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+version = "1.5.0"
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 optional = false
 python-versions = ">=3.8"
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 typing-extensions = ">=4.6.1"
 
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 [[package]]
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 exceptiongroup = {version = ">=1.0.0rc8", markers = "python_version < \"3.11\""}
 iniconfig = "*"
 packaging = "*"
-pluggy = ">=1.4,<2.0"
+pluggy = ">=1.5,<2.0"
 tomli = {version = ">=1", markers = "python_version < \"3.11\""}
 
 [package.extras]
-testing = ["argcomplete", "attrs (>=19.2)", "hypothesis (>=3.56)", "mock", "pygments (>=2.7.2)", "requests", "setuptools", "xmlschema"]
+dev = ["argcomplete", "attrs (>=19.2)", "hypothesis (>=3.56)", "mock", "pygments (>=2.7.2)", "requests", "setuptools", "xmlschema"]
 
 [[package]]
 name = "pytest-benchmark"
@@ -2108,6 +2223,20 @@ files = [
 [package.extras]
 cli = ["click (>=5.0)"]
 
+[[package]]
+name = "python-multipart"
+version = "0.0.9"
+description = "A streaming multipart parser for Python"
+optional = false
+python-versions = ">=3.8"
+files = [
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+
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+
 [[package]]
 name = "pytz"
 version = "2024.1"
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 [[package]]
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 ]
 
+[[package]]
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+python-versions = ">=3.8"
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+    {file = "ujson-5.9.0-pp310-pypy310_pp73-macosx_10_9_x86_64.whl", hash = "sha256:ffdfebd819f492e48e4f31c97cb593b9c1a8251933d8f8972e81697f00326ff1"},
+    {file = "ujson-5.9.0-pp310-pypy310_pp73-manylinux_2_17_aarch64.manylinux2014_aarch64.whl", hash = "sha256:c4eec2ddc046360d087cf35659c7ba0cbd101f32035e19047013162274e71fcf"},
+    {file = "ujson-5.9.0-pp310-pypy310_pp73-manylinux_2_17_x86_64.manylinux2014_x86_64.whl", hash = "sha256:2fbb90aa5c23cb3d4b803c12aa220d26778c31b6e4b7a13a1f49971f6c7d088e"},
+    {file = "ujson-5.9.0-pp310-pypy310_pp73-manylinux_2_5_i686.manylinux1_i686.manylinux_2_17_i686.manylinux2014_i686.whl", hash = "sha256:ba0823cb70866f0d6a4ad48d998dd338dce7314598721bc1b7986d054d782dfd"},
+    {file = "ujson-5.9.0-pp310-pypy310_pp73-win_amd64.whl", hash = "sha256:4e35d7885ed612feb6b3dd1b7de28e89baaba4011ecdf995e88be9ac614765e9"},
+    {file = "ujson-5.9.0-pp38-pypy38_pp73-macosx_10_9_x86_64.whl", hash = "sha256:b048aa93eace8571eedbd67b3766623e7f0acbf08ee291bef7d8106210432427"},
+    {file = "ujson-5.9.0-pp38-pypy38_pp73-manylinux_2_17_x86_64.manylinux2014_x86_64.whl", hash = "sha256:323279e68c195110ef85cbe5edce885219e3d4a48705448720ad925d88c9f851"},
+    {file = "ujson-5.9.0-pp38-pypy38_pp73-manylinux_2_5_i686.manylinux1_i686.manylinux_2_17_i686.manylinux2014_i686.whl", hash = "sha256:9ac92d86ff34296f881e12aa955f7014d276895e0e4e868ba7fddebbde38e378"},
+    {file = "ujson-5.9.0-pp38-pypy38_pp73-win_amd64.whl", hash = "sha256:6eecbd09b316cea1fd929b1e25f70382917542ab11b692cb46ec9b0a26c7427f"},
+    {file = "ujson-5.9.0-pp39-pypy39_pp73-macosx_10_9_x86_64.whl", hash = "sha256:473fb8dff1d58f49912323d7cb0859df5585cfc932e4b9c053bf8cf7f2d7c5c4"},
+    {file = "ujson-5.9.0-pp39-pypy39_pp73-manylinux_2_17_aarch64.manylinux2014_aarch64.whl", hash = "sha256:f91719c6abafe429c1a144cfe27883eace9fb1c09a9c5ef1bcb3ae80a3076a4e"},
+    {file = "ujson-5.9.0-pp39-pypy39_pp73-manylinux_2_17_x86_64.manylinux2014_x86_64.whl", hash = "sha256:7b1c0991c4fe256f5fdb19758f7eac7f47caac29a6c57d0de16a19048eb86bad"},
+    {file = "ujson-5.9.0-pp39-pypy39_pp73-manylinux_2_5_i686.manylinux1_i686.manylinux_2_17_i686.manylinux2014_i686.whl", hash = "sha256:2a8ea0f55a1396708e564595aaa6696c0d8af532340f477162ff6927ecc46e21"},
+    {file = "ujson-5.9.0-pp39-pypy39_pp73-win_amd64.whl", hash = "sha256:07e0cfdde5fd91f54cd2d7ffb3482c8ff1bf558abf32a8b953a5d169575ae1cd"},
+    {file = "ujson-5.9.0.tar.gz", hash = "sha256:89cc92e73d5501b8a7f48575eeb14ad27156ad092c2e9fc7e3cf949f07e75532"},
+]
+
 [[package]]
 name = "urllib3"
 version = "2.2.1"
diff --git a/tests/api/test_model.py b/tests/api/test_model.py
index 66cf56c6..d57d51a9 100644
--- a/tests/api/test_model.py
+++ b/tests/api/test_model.py
@@ -20,16 +20,16 @@ def test_index_model(test_mp, request):
         table_endpoint, json={"run": {"scenario": {"name__in": ["Scenario 1"]}}}
     )
 
-    assert res.json()["results"]["data"][0][1] == "Model 1"
+    assert res.json()["results"]["data"][0][0] == "Model 1"
 
     res = test_mp.backend.client.patch(
         table_endpoint, json={"run": {"scenario": {"name": "Scenario 2"}}}
     )
 
-    assert res.json()["results"]["data"][0][1] == "Model 2"
+    assert res.json()["results"]["data"][0][0] == "Model 2"
 
     res = test_mp.backend.client.patch(
         table_endpoint, json={"variable": {"name": "Variable 4"}}
     )
 
-    assert res.json()["results"]["data"][0][1] == "Model 2"
+    assert res.json()["results"]["data"][0][0] == "Model 2"
diff --git a/tests/api/test_scenario.py b/tests/api/test_scenario.py
index 3e29818c..956c65cd 100644
--- a/tests/api/test_scenario.py
+++ b/tests/api/test_scenario.py
@@ -20,16 +20,16 @@ def test_index_scenario(test_mp, request):
         table_endpoint, json={"run": {"model": {"name__in": ["Model 1"]}}}
     )
 
-    assert res.json()["results"]["data"][0][1] == "Scenario 1"
+    assert res.json()["results"]["data"][0][0] == "Scenario 1"
 
     res = test_mp.backend.client.patch(
         table_endpoint, json={"run": {"model": {"name": "Model 2"}}}
     )
 
-    assert res.json()["results"]["data"][0][1] == "Scenario 2"
+    assert res.json()["results"]["data"][0][0] == "Scenario 2"
 
     res = test_mp.backend.client.patch(
         table_endpoint, json={"variable": {"name": "Variable 4"}}
     )
 
-    assert res.json()["results"]["data"][0][1] == "Scenario 2"
+    assert res.json()["results"]["data"][0][0] == "Scenario 2"
diff --git a/tests/core/test_indexset.py b/tests/core/test_indexset.py
index 0260f191..ad7931ca 100644
--- a/tests/core/test_indexset.py
+++ b/tests/core/test_indexset.py
@@ -2,7 +2,7 @@
 import pandas.testing as pdt
 import pytest
 
-from ixmp4 import IndexSet
+from ixmp4 import IndexSet, Platform
 
 from ..utils import all_platforms
 
@@ -36,7 +36,7 @@ def df_from_list(indexsets: list[IndexSet]):
 @all_platforms
 class TestCoreIndexSet:
     def test_create_indexset(self, test_mp, request):
-        test_mp = request.getfixturevalue(test_mp)
+        test_mp: Platform = request.getfixturevalue(test_mp)  # type: ignore
         run = test_mp.runs.create("Model", "Scenario")
         indexset_1 = run.optimization.indexsets.create("IndexSet 1")
         assert indexset_1.id == 1
@@ -49,7 +49,7 @@ def test_create_indexset(self, test_mp, request):
             _ = run.optimization.indexsets.create("IndexSet 1")
 
     def test_get_indexset(self, test_mp, request):
-        test_mp = request.getfixturevalue(test_mp)
+        test_mp: Platform = request.getfixturevalue(test_mp)  # type: ignore
         run = test_mp.runs.create("Model", "Scenario")
         _ = run.optimization.indexsets.create("IndexSet 1")
         indexset = run.optimization.indexsets.get("IndexSet 1")
@@ -60,7 +60,7 @@ def test_get_indexset(self, test_mp, request):
             _ = run.optimization.indexsets.get("Foo")
 
     def test_add_elements(self, test_mp, request):
-        test_mp = request.getfixturevalue(test_mp)
+        test_mp: Platform = request.getfixturevalue(test_mp)  # type: ignore
         run = test_mp.runs.create("Model", "Scenario")
         test_elements = ["foo", "bar"]
         indexset_1 = run.optimization.indexsets.create("IndexSet 1")
@@ -88,7 +88,7 @@ def test_add_elements(self, test_mp, request):
         assert indexset_5.elements == test_elements_2
 
     def test_list_indexsets(self, test_mp, request):
-        test_mp = request.getfixturevalue(test_mp)
+        test_mp: Platform = request.getfixturevalue(test_mp)  # type: ignore
         run = test_mp.runs.create("Model", "Scenario")
         # Per default, list() lists only `default` version runs:
         run.set_as_default()
@@ -107,7 +107,7 @@ def test_list_indexsets(self, test_mp, request):
         assert not (set(expected_id) ^ set(list_id))
 
     def test_tabulate_indexsets(self, test_mp, request):
-        test_mp = request.getfixturevalue(test_mp)
+        test_mp: Platform = request.getfixturevalue(test_mp)  # type: ignore
         run = test_mp.runs.create("Model", "Scenario")
         # Per default, tabulate() lists only `default` version runs:
         run.set_as_default()
@@ -124,7 +124,7 @@ def test_tabulate_indexsets(self, test_mp, request):
         pdt.assert_frame_equal(expected, result)
 
     def test_indexset_docs(self, test_mp, request):
-        test_mp = request.getfixturevalue(test_mp)
+        test_mp: Platform = request.getfixturevalue(test_mp)  # type: ignore
         run = test_mp.runs.create("Model", "Scenario")
         indexset_1 = run.optimization.indexsets.create("IndexSet 1")
         docs = "Documentation of IndexSet 1"
diff --git a/tests/core/test_optimization_parameter.py b/tests/core/test_optimization_parameter.py
new file mode 100644
index 00000000..63a3da5d
--- /dev/null
+++ b/tests/core/test_optimization_parameter.py
@@ -0,0 +1,323 @@
+import pandas as pd
+import pytest
+
+from ixmp4 import Parameter, Platform
+
+from ..utils import all_platforms
+
+
+def df_from_list(parameters: list):
+    return pd.DataFrame(
+        [
+            [
+                parameter.run_id,
+                parameter.data,
+                parameter.name,
+                parameter.id,
+                parameter.created_at,
+                parameter.created_by,
+            ]
+            for parameter in parameters
+        ],
+        columns=[
+            "run__id",
+            "data",
+            "name",
+            "id",
+            "created_at",
+            "created_by",
+        ],
+    )
+
+
+@all_platforms
+class TestDataOptimizationParameter:
+    def test_create_parameter(self, test_mp, request):
+        test_mp: Platform = request.getfixturevalue(test_mp)  # type: ignore
+        run = test_mp.runs.create("Model", "Scenario")
+
+        # Test normal creation
+        indexset_1 = run.optimization.indexsets.create("Indexset")
+        parameter = run.optimization.parameters.create(
+            name="Parameter",
+            constrained_to_indexsets=["Indexset"],
+        )
+
+        assert parameter.run_id == run.id
+        assert parameter.name == "Parameter"
+        assert parameter.data == {}  # JsonDict type currently requires a dict, not None
+        assert parameter.columns[0].name == "Indexset"
+        assert parameter.constrained_to_indexsets == [indexset_1.name]
+        assert parameter.values == []
+        assert parameter.units == []
+
+        # Test duplicate name raises
+        with pytest.raises(Parameter.NotUnique):
+            _ = run.optimization.parameters.create(
+                "Parameter", constrained_to_indexsets=["Indexset"]
+            )
+
+        # Test mismatch in constrained_to_indexsets and column_names raises
+        with pytest.raises(ValueError, match="not equal in length"):
+            _ = run.optimization.parameters.create(
+                "Parameter 2",
+                constrained_to_indexsets=["Indexset"],
+                column_names=["Dimension 1", "Dimension 2"],
+            )
+
+        # Test columns_names are used for names if given
+        parameter_2 = run.optimization.parameters.create(
+            "Parameter 2",
+            constrained_to_indexsets=[indexset_1.name],
+            column_names=["Column 1"],
+        )
+        assert parameter_2.columns[0].name == "Column 1"
+
+        # Test duplicate column_names raise
+        with pytest.raises(ValueError, match="`column_names` are not unique"):
+            _ = run.optimization.parameters.create(
+                name="Parameter 3",
+                constrained_to_indexsets=[indexset_1.name, indexset_1.name],
+                column_names=["Column 1", "Column 1"],
+            )
+
+        # Test column.dtype is registered correctly
+        indexset_2 = run.optimization.indexsets.create("Indexset 2")
+        indexset_2.add(elements=2024)
+        parameter_3 = run.optimization.parameters.create(
+            "Parameter 5",
+            constrained_to_indexsets=["Indexset", indexset_2.name],
+        )
+        # If indexset doesn't have elements, a generic dtype is registered
+        assert parameter_3.columns[0].dtype == "object"
+        assert parameter_3.columns[1].dtype == "int64"
+
+    def test_get_parameter(self, test_mp, request):
+        test_mp: Platform = request.getfixturevalue(test_mp)  # type: ignore
+        run = test_mp.runs.create("Model", "Scenario")
+        indexset = run.optimization.indexsets.create("Indexset")
+        _ = run.optimization.parameters.create(
+            name="Parameter", constrained_to_indexsets=["Indexset"]
+        )
+        parameter = run.optimization.parameters.get(name="Parameter")
+        assert parameter.run_id == run.id
+        assert parameter.id == 1
+        assert parameter.name == "Parameter"
+        assert parameter.data == {}
+        assert parameter.values == []
+        assert parameter.units == []
+        assert parameter.columns[0].name == indexset.name
+        assert parameter.constrained_to_indexsets == [indexset.name]
+
+        with pytest.raises(Parameter.NotFound):
+            _ = run.optimization.parameters.get("Parameter 2")
+
+    def test_parameter_add_data(self, test_mp, request):
+        test_mp: Platform = request.getfixturevalue(test_mp)  # type: ignore
+        run = test_mp.runs.create("Model", "Scenario")
+        unit = test_mp.units.create("Unit")
+        indexset_1 = run.optimization.indexsets.create("Indexset")
+        indexset_1.add(elements=["foo", "bar", ""])
+        indexset_2 = run.optimization.indexsets.create("Indexset 2")
+        indexset_2.add(elements=[1, 2, 3])
+        # pandas can only convert dicts to dataframes if the values are lists
+        # or if index is given. But maybe using read_json instead of from_dict
+        # can remedy this. Or maybe we want to catch the resulting
+        # "ValueError: If using all scalar values, you must pass an index" and
+        # reraise a custom informative error?
+        test_data_1 = {
+            "Indexset": ["foo"],
+            "Indexset 2": [1],
+            "values": [3.14],
+            "units": [unit.name],
+        }
+        parameter = run.optimization.parameters.create(
+            "Parameter",
+            constrained_to_indexsets=[indexset_1.name, indexset_2.name],
+        )
+        parameter.add(data=test_data_1)
+        assert parameter.data == test_data_1
+        assert parameter.values == test_data_1["values"]
+        assert parameter.units == test_data_1["units"]
+
+        parameter_2 = run.optimization.parameters.create(
+            name="Parameter 2",
+            constrained_to_indexsets=[indexset_1.name, indexset_2.name],
+        )
+
+        with pytest.raises(
+            AssertionError, match=r"must include the column\(s\): values!"
+        ):
+            parameter_2.add(
+                pd.DataFrame(
+                    {
+                        "Indexset": [None],
+                        "Indexset 2": [2],
+                        "units": [unit.name],
+                    }
+                ),
+            )
+
+        with pytest.raises(
+            AssertionError, match=r"must include the column\(s\): units!"
+        ):
+            parameter_2.add(
+                data=pd.DataFrame(
+                    {
+                        "Indexset": [None],
+                        "Indexset 2": [2],
+                        "values": [""],
+                    }
+                ),
+            )
+
+        # By converting data to pd.DataFrame, we automatically enforce equal length
+        # of new columns, raises All arrays must be of the same length otherwise:
+        with pytest.raises(ValueError, match="All arrays must be of the same length"):
+            parameter_2.add(
+                data={
+                    "Indexset": ["foo", "foo"],
+                    "Indexset 2": [2, 2],
+                    "values": [1, 2],
+                    "units": [unit.name],
+                },
+            )
+
+        with pytest.raises(ValueError, match="contains duplicate rows"):
+            parameter_2.add(
+                data={
+                    "Indexset": ["foo", "foo"],
+                    "Indexset 2": [2, 2],
+                    "values": [1, 2],
+                    "units": [unit.name, unit.name],
+                },
+            )
+
+        # Test that order is conserved
+        test_data_2 = {
+            "Indexset": ["", "", "foo", "foo", "bar", "bar"],
+            "Indexset 2": [3, 1, 2, 1, 2, 3],
+            "values": [6, 5, 4, 3, 2, 1],
+            "units": [unit.name] * 6,
+        }
+        parameter_2.add(test_data_2)
+        assert parameter_2.data == test_data_2
+        assert parameter_2.values == test_data_2["values"]
+        assert parameter_2.units == test_data_2["units"]
+
+        # Test order is conserved with varying types and upon later addition of data
+        parameter_3 = run.optimization.parameters.create(
+            name="Parameter 3",
+            constrained_to_indexsets=[indexset_1.name, indexset_2.name],
+            column_names=["Column 1", "Column 2"],
+        )
+        unit_2 = test_mp.units.create("Unit 2")
+        unit_3 = test_mp.units.create("Unit 3")
+
+        test_data_3 = {
+            "Column 1": ["bar", "foo", ""],
+            "Column 2": [2, 3, 1],
+            "values": ["3", 2.0, 1],
+            "units": [unit_3.name, unit_2.name, unit.name],
+        }
+        parameter_3.add(data=test_data_3)
+        assert parameter_3.data == test_data_3
+        assert parameter_3.values == test_data_3["values"]
+        assert parameter_3.units == test_data_3["units"]
+
+        test_data_4 = {
+            "Column 1": ["foo", "", "bar"],
+            "Column 2": [2, 3, 1],
+            "values": [3.14, 2, "1"],
+            "units": [unit_2.name, unit.name, unit_3.name],
+        }
+        parameter_3.add(data=test_data_4)
+        test_data_5 = test_data_3.copy()
+        for key, value in test_data_4.items():
+            test_data_5[key].extend(value)
+        assert parameter_3.data == test_data_5
+        assert parameter_3.values == test_data_5["values"]
+        assert parameter_3.units == test_data_5["units"]
+
+    def test_list_parameter(self, test_mp, request):
+        test_mp: Platform = request.getfixturevalue(test_mp)  # type: ignore
+        run = test_mp.runs.create("Model", "Scenario")
+        # Per default, list() lists scalars for `default` version runs:
+        run.set_as_default()
+        _ = run.optimization.indexsets.create("Indexset")
+        _ = run.optimization.indexsets.create("Indexset 2")
+        parameter = run.optimization.parameters.create(
+            "Parameter", constrained_to_indexsets=["Indexset"]
+        )
+        parameter_2 = run.optimization.parameters.create(
+            "Parameter 2", constrained_to_indexsets=["Indexset 2"]
+        )
+        expected_ids = [parameter.id, parameter_2.id]
+        list_ids = [parameter.id for parameter in run.optimization.parameters.list()]
+        assert not (set(expected_ids) ^ set(list_ids))
+
+        # Test retrieving just one result by providing a name
+        expected_id = [parameter.id]
+        list_id = [
+            parameter.id
+            for parameter in run.optimization.parameters.list(name="Parameter")
+        ]
+        assert not (set(expected_id) ^ set(list_id))
+
+    def test_tabulate_parameter(self, test_mp, request):
+        test_mp: Platform = request.getfixturevalue(test_mp)  # type: ignore
+        run = test_mp.runs.create("Model", "Scenario")
+        # Per default, tabulate() lists scalars for `default` version runs:
+        run.set_as_default()
+        indexset = run.optimization.indexsets.create("Indexset")
+        indexset_2 = run.optimization.indexsets.create("Indexset 2")
+        parameter = run.optimization.parameters.create(
+            name="Parameter",
+            constrained_to_indexsets=["Indexset", "Indexset 2"],
+        )
+        parameter_2 = run.optimization.parameters.create(
+            name="Parameter 2",
+            constrained_to_indexsets=["Indexset", "Indexset 2"],
+        )
+        pd.testing.assert_frame_equal(
+            df_from_list([parameter_2]),
+            run.optimization.parameters.tabulate(name="Parameter 2"),
+        )
+
+        unit = test_mp.units.create("Unit")
+        unit_2 = test_mp.units.create("Unit 2")
+        indexset.add(elements=["foo", "bar"])
+        indexset_2.add(elements=[1, 2, 3])
+        test_data_1 = {
+            "Indexset": ["foo"],
+            "Indexset 2": [1],
+            "values": ["value"],
+            "units": [unit.name],
+        }
+        parameter.add(data=test_data_1)
+
+        test_data_2 = {
+            "Indexset 2": [2, 3],
+            "Indexset": ["foo", "bar"],
+            "values": [1, "value"],
+            "units": [unit.name, unit_2.name],
+        }
+        parameter_2.add(data=test_data_2)
+        pd.testing.assert_frame_equal(
+            df_from_list([parameter, parameter_2]),
+            run.optimization.parameters.tabulate(),
+        )
+
+    def test_parameter_docs(self, test_mp, request):
+        test_mp: Platform = request.getfixturevalue(test_mp)  # type: ignore
+        run = test_mp.runs.create("Model", "Scenario")
+        indexset = run.optimization.indexsets.create("Indexset")
+        parameter_1 = run.optimization.parameters.create(
+            "Parameter 1", constrained_to_indexsets=[indexset.name]
+        )
+        docs = "Documentation of Parameter 1"
+        parameter_1.docs = docs
+        assert parameter_1.docs == docs
+
+        parameter_1.docs = None
+        assert parameter_1.docs is None
diff --git a/tests/data/test_docs.py b/tests/data/test_docs.py
index d23c0b8a..6abfe5e4 100644
--- a/tests/data/test_docs.py
+++ b/tests/data/test_docs.py
@@ -1,5 +1,6 @@
 import pytest
 
+from ixmp4 import Platform
 from ixmp4.data.abstract import Docs
 
 from ..utils import all_platforms
@@ -8,7 +9,7 @@
 @all_platforms
 class TestDataDocs:
     def test_get_and_set_modeldocs(self, test_mp, request):
-        test_mp = request.getfixturevalue(test_mp)
+        test_mp: Platform = request.getfixturevalue(test_mp)  # type: ignore
         model = test_mp.backend.models.create("Model")
 
         docs_model = test_mp.backend.models.docs.set(model.id, "Description of Model")
@@ -16,7 +17,7 @@ def test_get_and_set_modeldocs(self, test_mp, request):
         assert docs_model == docs_model1
 
     def test_change_empty_modeldocs(self, test_mp, request):
-        test_mp = request.getfixturevalue(test_mp)
+        test_mp: Platform = request.getfixturevalue(test_mp)  # type: ignore
         model = test_mp.backend.models.create("Model")
 
         with pytest.raises(Docs.NotFound):
@@ -35,7 +36,7 @@ def test_change_empty_modeldocs(self, test_mp, request):
         assert test_mp.backend.models.docs.get(model.id) == docs_model2
 
     def test_delete_modeldocs(self, test_mp, request):
-        test_mp = request.getfixturevalue(test_mp)
+        test_mp: Platform = request.getfixturevalue(test_mp)  # type: ignore
         model = test_mp.backend.models.create("Model")
         docs_model = test_mp.backend.models.docs.set(
             model.id, "Description of test Model"
@@ -49,7 +50,7 @@ def test_delete_modeldocs(self, test_mp, request):
             test_mp.backend.models.docs.get(model.id)
 
     def test_get_and_set_regiondocs(self, test_mp, request):
-        test_mp = request.getfixturevalue(test_mp)
+        test_mp: Platform = request.getfixturevalue(test_mp)  # type: ignore
         region = test_mp.backend.regions.create("Region", "Hierarchy")
         docs_region = test_mp.backend.regions.docs.set(
             region.id, "Description of test Region"
@@ -59,7 +60,7 @@ def test_get_and_set_regiondocs(self, test_mp, request):
         assert docs_region == docs_region1
 
     def test_change_empty_regiondocs(self, test_mp, request):
-        test_mp = request.getfixturevalue(test_mp)
+        test_mp: Platform = request.getfixturevalue(test_mp)  # type: ignore
         region = test_mp.backend.regions.create("Region", "Hierarchy")
 
         with pytest.raises(Docs.NotFound):
@@ -78,7 +79,7 @@ def test_change_empty_regiondocs(self, test_mp, request):
         assert test_mp.backend.regions.docs.get(region.id) == docs_region2
 
     def test_delete_regiondocs(self, test_mp, request):
-        test_mp = request.getfixturevalue(test_mp)
+        test_mp: Platform = request.getfixturevalue(test_mp)  # type: ignore
         region = test_mp.backend.regions.create("Region", "Hierarchy")
         docs_region = test_mp.backend.regions.docs.set(
             region.id, "Description of test region"
@@ -92,7 +93,7 @@ def test_delete_regiondocs(self, test_mp, request):
             test_mp.backend.regions.docs.get(region.id)
 
     def test_get_and_set_scenariodocs(self, test_mp, request):
-        test_mp = request.getfixturevalue(test_mp)
+        test_mp: Platform = request.getfixturevalue(test_mp)  # type: ignore
         scenario = test_mp.backend.scenarios.create("Scenario")
         docs_scenario = test_mp.backend.scenarios.docs.set(
             scenario.id, "Description of Scenario"
@@ -101,7 +102,7 @@ def test_get_and_set_scenariodocs(self, test_mp, request):
         assert docs_scenario == docs_scenario1
 
     def test_change_empty_scenariodocs(self, test_mp, request):
-        test_mp = request.getfixturevalue(test_mp)
+        test_mp: Platform = request.getfixturevalue(test_mp)  # type: ignore
         scenario = test_mp.backend.scenarios.create("Scenario")
 
         with pytest.raises(Docs.NotFound):
@@ -120,7 +121,7 @@ def test_change_empty_scenariodocs(self, test_mp, request):
         assert test_mp.backend.scenarios.docs.get(scenario.id) == docs_scenario2
 
     def test_delete_scenariodocs(self, test_mp, request):
-        test_mp = request.getfixturevalue(test_mp)
+        test_mp: Platform = request.getfixturevalue(test_mp)  # type: ignore
         scenario = test_mp.backend.scenarios.create("Scenario")
         docs_scenario = test_mp.backend.scenarios.docs.set(
             scenario.id, "Description of test Scenario"
@@ -134,7 +135,7 @@ def test_delete_scenariodocs(self, test_mp, request):
             test_mp.backend.scenarios.docs.get(scenario.id)
 
     def test_get_and_set_unitdocs(self, test_mp, request):
-        test_mp = request.getfixturevalue(test_mp)
+        test_mp: Platform = request.getfixturevalue(test_mp)  # type: ignore
         unit = test_mp.backend.units.create("Unit")
         docs_unit = test_mp.backend.units.docs.set(unit.id, "Description of test Unit")
         docs_unit1 = test_mp.backend.units.docs.get(unit.id)
@@ -142,7 +143,7 @@ def test_get_and_set_unitdocs(self, test_mp, request):
         assert docs_unit == docs_unit1
 
     def test_change_empty_unitdocs(self, test_mp, request):
-        test_mp = request.getfixturevalue(test_mp)
+        test_mp: Platform = request.getfixturevalue(test_mp)  # type: ignore
         unit = test_mp.backend.units.create("Unit")
 
         with pytest.raises(Docs.NotFound):
@@ -159,7 +160,7 @@ def test_change_empty_unitdocs(self, test_mp, request):
         assert test_mp.backend.units.docs.get(unit.id) == docs_unit2
 
     def test_delete_unitdocs(self, test_mp, request):
-        test_mp = request.getfixturevalue(test_mp)
+        test_mp: Platform = request.getfixturevalue(test_mp)  # type: ignore
         unit = test_mp.backend.units.create("Unit")
         docs_unit = test_mp.backend.units.docs.set(unit.id, "Description of test Unit")
 
@@ -171,7 +172,7 @@ def test_delete_unitdocs(self, test_mp, request):
             test_mp.backend.units.docs.get(unit.id)
 
     def test_get_and_set_variabledocs(self, test_mp, request):
-        test_mp = request.getfixturevalue(test_mp)
+        test_mp: Platform = request.getfixturevalue(test_mp)  # type: ignore
         variable = test_mp.backend.iamc.variables.create("Variable")
         docs_variable = test_mp.backend.iamc.variables.docs.set(
             variable.id, "Description of test Variable"
@@ -181,7 +182,7 @@ def test_get_and_set_variabledocs(self, test_mp, request):
         assert docs_variable == docs_variables1
 
     def test_change_empty_variabledocs(self, test_mp, request):
-        test_mp = request.getfixturevalue(test_mp)
+        test_mp: Platform = request.getfixturevalue(test_mp)  # type: ignore
         variable = test_mp.backend.iamc.variables.create("Variable")
 
         with pytest.raises(Docs.NotFound):
@@ -200,7 +201,7 @@ def test_change_empty_variabledocs(self, test_mp, request):
         assert test_mp.backend.iamc.variables.docs.get(variable.id) == docs_variable2
 
     def test_delete_variabledocs(self, test_mp, request):
-        test_mp = request.getfixturevalue(test_mp)
+        test_mp: Platform = request.getfixturevalue(test_mp)  # type: ignore
         variable = test_mp.backend.iamc.variables.create("Variable")
         docs_variable = test_mp.backend.iamc.variables.docs.set(
             variable.id, "Description of test Variable"
@@ -214,7 +215,7 @@ def test_delete_variabledocs(self, test_mp, request):
             test_mp.backend.iamc.variables.docs.get(variable.id)
 
     def test_get_and_set_indexsetdocs(self, test_mp, request):
-        test_mp = request.getfixturevalue(test_mp)
+        test_mp: Platform = request.getfixturevalue(test_mp)  # type: ignore
         run = test_mp.backend.runs.create("Model", "Scenario")
         indexset = test_mp.backend.optimization.indexsets.create(
             run_id=run.id, name="IndexSet"
@@ -227,7 +228,7 @@ def test_get_and_set_indexsetdocs(self, test_mp, request):
         assert docs_indexset == docs_indexset1
 
     def test_change_empty_indexsetdocs(self, test_mp, request):
-        test_mp = request.getfixturevalue(test_mp)
+        test_mp: Platform = request.getfixturevalue(test_mp)  # type: ignore
         run = test_mp.backend.runs.create("Model", "Scenario")
         indexset = test_mp.backend.optimization.indexsets.create(
             run_id=run.id, name="IndexSet"
@@ -255,7 +256,7 @@ def test_change_empty_indexsetdocs(self, test_mp, request):
         )
 
     def test_delete_indexsetdocs(self, test_mp, request):
-        test_mp = request.getfixturevalue(test_mp)
+        test_mp: Platform = request.getfixturevalue(test_mp)  # type: ignore
         run = test_mp.backend.runs.create("Model", "Scenario")
         indexset = test_mp.backend.optimization.indexsets.create(
             run_id=run.id, name="IndexSet"
@@ -275,7 +276,7 @@ def test_delete_indexsetdocs(self, test_mp, request):
             test_mp.backend.optimization.indexsets.docs.get(indexset.id)
 
     def test_get_and_set_scalardocs(self, test_mp, request):
-        test_mp = request.getfixturevalue(test_mp)
+        test_mp: Platform = request.getfixturevalue(test_mp)  # type: ignore
         run = test_mp.backend.runs.create("Model", "Scenario")
         unit = test_mp.backend.units.create("Unit")
         scalar = test_mp.backend.optimization.scalars.create(
@@ -289,7 +290,7 @@ def test_get_and_set_scalardocs(self, test_mp, request):
         assert docs_scalar == docs_scalar1
 
     def test_change_empty_scalardocs(self, test_mp, request):
-        test_mp = request.getfixturevalue(test_mp)
+        test_mp: Platform = request.getfixturevalue(test_mp)  # type: ignore
         run = test_mp.backend.runs.create("Model", "Scenario")
         unit = test_mp.backend.units.create("Unit")
         scalar = test_mp.backend.optimization.scalars.create(
@@ -312,7 +313,7 @@ def test_change_empty_scalardocs(self, test_mp, request):
         assert test_mp.backend.optimization.scalars.docs.get(scalar.id) == docs_scalar2
 
     def test_delete_scalardocs(self, test_mp, request):
-        test_mp = request.getfixturevalue(test_mp)
+        test_mp: Platform = request.getfixturevalue(test_mp)  # type: ignore
         run = test_mp.backend.runs.create("Model", "Scenario")
         unit = test_mp.backend.units.create("Unit")
         scalar = test_mp.backend.optimization.scalars.create(
@@ -330,7 +331,7 @@ def test_delete_scalardocs(self, test_mp, request):
             test_mp.backend.optimization.scalars.docs.get(scalar.id)
 
     def test_get_and_set_tabledocs(self, test_mp, request):
-        test_mp = request.getfixturevalue(test_mp)
+        test_mp: Platform = request.getfixturevalue(test_mp)  # type: ignore
         run = test_mp.backend.runs.create("Model", "Scenario")
         _ = test_mp.backend.optimization.indexsets.create(
             run_id=run.id, name="Indexset"
@@ -346,7 +347,7 @@ def test_get_and_set_tabledocs(self, test_mp, request):
         assert docs_table == docs_table1
 
     def test_change_empty_tabledocs(self, test_mp, request):
-        test_mp = request.getfixturevalue(test_mp)
+        test_mp: Platform = request.getfixturevalue(test_mp)  # type: ignore
         run = test_mp.backend.runs.create("Model", "Scenario")
         _ = test_mp.backend.optimization.indexsets.create(
             run_id=run.id, name="Indexset"
@@ -371,7 +372,7 @@ def test_change_empty_tabledocs(self, test_mp, request):
         assert test_mp.backend.optimization.tables.docs.get(table.id) == docs_table2
 
     def test_delete_tabledocs(self, test_mp, request):
-        test_mp = request.getfixturevalue(test_mp)
+        test_mp: Platform = request.getfixturevalue(test_mp)  # type: ignore
         run = test_mp.backend.runs.create("Model", "Scenario")
         _ = test_mp.backend.optimization.indexsets.create(
             run_id=run.id, name="Indexset"
@@ -389,3 +390,73 @@ def test_delete_tabledocs(self, test_mp, request):
 
         with pytest.raises(Docs.NotFound):
             test_mp.backend.optimization.tables.docs.get(table.id)
+
+    def test_get_and_set_parameterdocs(self, test_mp, request):
+        test_mp: Platform = request.getfixturevalue(test_mp)  # type: ignore
+        run = test_mp.backend.runs.create("Model", "Scenario")
+        _ = test_mp.backend.optimization.indexsets.create(
+            run_id=run.id, name="Indexset"
+        )
+        parameter = test_mp.backend.optimization.parameters.create(
+            run_id=run.id, name="Parameter", constrained_to_indexsets=["Indexset"]
+        )
+        docs_parameter = test_mp.backend.optimization.parameters.docs.set(
+            parameter.id, "Description of test Parameter"
+        )
+        docs_parameter1 = test_mp.backend.optimization.parameters.docs.get(parameter.id)
+
+        assert docs_parameter == docs_parameter1
+
+    def test_change_empty_parameterdocs(self, test_mp, request):
+        test_mp: Platform = request.getfixturevalue(test_mp)  # type: ignore
+        run = test_mp.backend.runs.create("Model", "Scenario")
+        _ = test_mp.backend.optimization.indexsets.create(
+            run_id=run.id, name="Indexset"
+        )
+        parameter = test_mp.backend.optimization.parameters.create(
+            run_id=run.id, name="Parameter", constrained_to_indexsets=["Indexset"]
+        )
+
+        with pytest.raises(Docs.NotFound):
+            test_mp.backend.optimization.parameters.docs.get(parameter.id)
+
+        docs_parameter1 = test_mp.backend.optimization.parameters.docs.set(
+            parameter.id, "Description of test Parameter"
+        )
+
+        assert (
+            test_mp.backend.optimization.parameters.docs.get(parameter.id)
+            == docs_parameter1
+        )
+
+        docs_parameter2 = test_mp.backend.optimization.parameters.docs.set(
+            parameter.id, "Different description of test Parameter"
+        )
+
+        assert (
+            test_mp.backend.optimization.parameters.docs.get(parameter.id)
+            == docs_parameter2
+        )
+
+    def test_delete_parameterdocs(self, test_mp, request):
+        test_mp: Platform = request.getfixturevalue(test_mp)  # type: ignore
+        run = test_mp.backend.runs.create("Model", "Scenario")
+        _ = test_mp.backend.optimization.indexsets.create(
+            run_id=run.id, name="Indexset"
+        )
+        parameter = test_mp.backend.optimization.parameters.create(
+            run_id=run.id, name="Parameter", constrained_to_indexsets=["Indexset"]
+        )
+        docs_parameter = test_mp.backend.optimization.parameters.docs.set(
+            parameter.id, "Description of test Parameter"
+        )
+
+        assert (
+            test_mp.backend.optimization.parameters.docs.get(parameter.id)
+            == docs_parameter
+        )
+
+        test_mp.backend.optimization.parameters.docs.delete(parameter.id)
+
+        with pytest.raises(Docs.NotFound):
+            test_mp.backend.optimization.parameters.docs.get(parameter.id)
diff --git a/tests/data/test_optimization_parameter.py b/tests/data/test_optimization_parameter.py
index 9dffc28a..260539f6 100644
--- a/tests/data/test_optimization_parameter.py
+++ b/tests/data/test_optimization_parameter.py
@@ -3,34 +3,34 @@
 
 from ixmp4 import Parameter, Platform
 
-from ..utils import database_platforms
+from ..utils import all_platforms
 
 
 def df_from_list(parameters: list):
     return pd.DataFrame(
         [
             [
-                parameter.name,
-                parameter.data,
                 parameter.run__id,
+                parameter.data,
+                parameter.name,
+                parameter.id,
                 parameter.created_at,
                 parameter.created_by,
-                parameter.id,
             ]
             for parameter in parameters
         ],
         columns=[
-            "name",
-            "data",
             "run__id",
+            "data",
+            "name",
+            "id",
             "created_at",
             "created_by",
-            "id",
         ],
     )
 
 
-@database_platforms
+@all_platforms
 class TestDataOptimizationParameter:
     def test_create_parameter(self, test_mp, request):
         test_mp: Platform = request.getfixturevalue(test_mp)  # type: ignore
@@ -275,80 +275,92 @@ def test_parameter_add_data(self, test_mp, request):
             test_data_5[key].extend(value)
         assert parameter_3.data == test_data_5
 
-    # def test_list_parameter(self, test_mp, request):
-    #     test_mp = request.getfixturevalue(test_mp)
-    #     run = test_mp.backend.runs.create("Model", "Scenario")
-    #     # Per default, list() lists scalars for `default` version runs:
-    #     test_mp.backend.runs.set_as_default_version(run.id)
-    #     _ = test_mp.backend.optimization.indexsets.create(
-    #         run_id=run.id, name="Indexset"
-    #     )
-    #     _ = test_mp.backend.optimization.indexsets.create(
-    #         run_id=run.id, name="Indexset 2"
-    #     )
-    #     parameter = test_mp.backend.optimization.parameters.create(
-    #         run_id=run.id, name="Parameter", constrained_to_indexsets=["Indexset"]
-    #     )
-    #     parameter_2 = test_mp.backend.optimization.parameters.create(
-    #         run_id=run.id, name="Parameter 2", constrained_to_indexsets=["Indexset 2"]
-    #     )
-    #     assert [
-    #         parameter,
-    #         parameter_2,
-    #     ] == test_mp.backend.optimization.parameters.list()
+    def test_list_parameter(self, test_mp, request):
+        test_mp: Platform = request.getfixturevalue(test_mp)  # type: ignore
+        run = test_mp.backend.runs.create("Model", "Scenario")
+        # Per default, list() lists scalars for `default` version runs:
+        test_mp.backend.runs.set_as_default_version(run.id)
+        _ = test_mp.backend.optimization.indexsets.create(
+            run_id=run.id, name="Indexset"
+        )
+        _ = test_mp.backend.optimization.indexsets.create(
+            run_id=run.id, name="Indexset 2"
+        )
+        parameter = test_mp.backend.optimization.parameters.create(
+            run_id=run.id, name="Parameter", constrained_to_indexsets=["Indexset"]
+        )
+        parameter_2 = test_mp.backend.optimization.parameters.create(
+            run_id=run.id, name="Parameter 2", constrained_to_indexsets=["Indexset 2"]
+        )
+        assert [
+            parameter,
+            parameter_2,
+        ] == test_mp.backend.optimization.parameters.list()
 
-    #     assert [parameter] == test_mp.backend.optimization.parameters.list(
-    #         name="Parameter"
-    #     )
+        assert [parameter] == test_mp.backend.optimization.parameters.list(
+            name="Parameter"
+        )
 
-    # def test_tabulate_parameter(self, test_mp, request):
-    #     test_mp: Platform = request.getfixturevalue(test_mp)  # type: ignore
-    #     run = test_mp.backend.runs.create("Model", "Scenario")
-    #     # Per default, tabulate() lists scalars for `default` version runs:
-    #     test_mp.backend.runs.set_as_default_version(run.id)
-    #     indexset = test_mp.backend.optimization.indexsets.create(
-    #         run_id=run.id, name="Indexset"
-    #     )
-    #     indexset_2 = test_mp.backend.optimization.indexsets.create(
-    #         run_id=run.id, name="Indexset 2"
-    #     )
-    #     parameter = test_mp.backend.optimization.parameters.create(
-    #         run_id=run.id,
-    #         name="Parameter",
-    #         constrained_to_indexsets=["Indexset", "Indexset 2"],
-    #     )
-    #     parameter_2 = test_mp.backend.optimization.parameters.create(
-    #         run_id=run.id,
-    #         name="Parameter 2",
-    #         constrained_to_indexsets=["Indexset", "Indexset 2"],
-    #     )
-    #     pd.testing.assert_frame_equal(
-    #         df_from_list([parameter_2]),
-    #         test_mp.backend.optimization.parameters.tabulate(name="Parameter 2"),
-    #     )
+    def test_tabulate_parameter(self, test_mp, request):
+        test_mp: Platform = request.getfixturevalue(test_mp)  # type: ignore
+        run = test_mp.backend.runs.create("Model", "Scenario")
+        # Per default, tabulate() lists scalars for `default` version runs:
+        test_mp.backend.runs.set_as_default_version(run.id)
+        indexset = test_mp.backend.optimization.indexsets.create(
+            run_id=run.id, name="Indexset"
+        )
+        indexset_2 = test_mp.backend.optimization.indexsets.create(
+            run_id=run.id, name="Indexset 2"
+        )
+        parameter = test_mp.backend.optimization.parameters.create(
+            run_id=run.id,
+            name="Parameter",
+            constrained_to_indexsets=["Indexset", "Indexset 2"],
+        )
+        parameter_2 = test_mp.backend.optimization.parameters.create(
+            run_id=run.id,
+            name="Parameter 2",
+            constrained_to_indexsets=["Indexset", "Indexset 2"],
+        )
+        pd.testing.assert_frame_equal(
+            df_from_list([parameter_2]),
+            test_mp.backend.optimization.parameters.tabulate(name="Parameter 2"),
+        )
 
-    #     test_mp.backend.optimization.indexsets.add_elements(
-    #         indexset_id=indexset.id, elements=["foo", "bar"]
-    #     )
-    #     test_mp.backend.optimization.indexsets.add_elements(
-    #         indexset_id=indexset_2.id, elements=[1, 2, 3]
-    #     )
-    #     test_data_1 = {"Indexset": ["foo"], "Indexset 2": [1]}
-    #     test_mp.backend.optimization.parameters.add_data(
-    #         parameter_id=parameter.id, data=test_data_1
-    #     )
-    #     parameter = test_mp.backend.optimization.parameters.get(
-    #         run_id=run.id, name="Parameter"
-    #     )
+        unit = test_mp.backend.units.create("Unit")
+        unit_2 = test_mp.backend.units.create("Unit 2")
+        test_mp.backend.optimization.indexsets.add_elements(
+            indexset_id=indexset.id, elements=["foo", "bar"]
+        )
+        test_mp.backend.optimization.indexsets.add_elements(
+            indexset_id=indexset_2.id, elements=[1, 2, 3]
+        )
+        test_data_1 = {
+            "Indexset": ["foo"],
+            "Indexset 2": [1],
+            "values": ["value"],
+            "units": [unit.name],
+        }
+        test_mp.backend.optimization.parameters.add_data(
+            parameter_id=parameter.id, data=test_data_1
+        )
+        parameter = test_mp.backend.optimization.parameters.get(
+            run_id=run.id, name="Parameter"
+        )
 
-    #     test_data_2 = {"Indexset 2": [2, 3], "Indexset": ["foo", "bar"]}
-    #     test_mp.backend.optimization.parameters.add_data(
-    #         parameter_id=parameter_2.id, data=test_data_2
-    #     )
-    #     parameter_2 = test_mp.backend.optimization.parameters.get(
-    #         run_id=run.id, name="Parameter 2"
-    #     )
-    #     pd.testing.assert_frame_equal(
-    #         df_from_list([parameter, parameter_2]),
-    #         test_mp.backend.optimization.parameters.tabulate(),
-    #     )
+        test_data_2 = {
+            "Indexset 2": [2, 3],
+            "Indexset": ["foo", "bar"],
+            "values": [1, "value"],
+            "units": [unit.name, unit_2.name],
+        }
+        test_mp.backend.optimization.parameters.add_data(
+            parameter_id=parameter_2.id, data=test_data_2
+        )
+        parameter_2 = test_mp.backend.optimization.parameters.get(
+            run_id=run.id, name="Parameter 2"
+        )
+        pd.testing.assert_frame_equal(
+            df_from_list([parameter, parameter_2]),
+            test_mp.backend.optimization.parameters.tabulate(),
+        )