diff --git a/CHANGELOG.md b/CHANGELOG.md
index acb2bbe4..0eb78e8a 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -57,6 +57,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 - Updated the processes based on the subtypes `raster-cube` or `vector-cube` to work with the subtype `datacube` instead. [#68](https://github.com/Open-EO/openeo-processes/issues/68)
 - `sort` and `order`: The ordering of ties is not defined anymore. [#409](https://github.com/Open-EO/openeo-processes/issues/409)
 - `quantiles`: Parameter `probabilities` provided as array must be in ascending order. [#297](https://github.com/Open-EO/openeo-processes/pull/297)
+- `fit_curve` and `predict_curve`: Heavily modified specifications. `fit_curve` works on arrays instead of data cubes, `predict_curve` doesn't support gap filling anymore, clarify no-data handling, ... [#425](https://github.com/Open-EO/openeo-processes/issues/425)
 - `climatological_normal`: The `climatology_period` parameter accepts an array of integers instead of strings. [#331](https://github.com/Open-EO/openeo-processes/issues/331)
 
 ### Deprecated
diff --git a/proposals/fit_curve.json b/proposals/fit_curve.json
index 5d33b652..aafb917e 100644
--- a/proposals/fit_curve.json
+++ b/proposals/fit_curve.json
@@ -1,38 +1,34 @@
 {
     "id": "fit_curve",
     "summary": "Curve fitting",
-    "description": "Use non-linear least squares to fit a model function `y = f(x, parameters)` to data.\n\nThe process throws an `InvalidValues` exception if invalid values are encountered. Valid values are finite numbers (see also ``is_valid()``).",
+    "description": "Use non-linear least squares to fit a model function `y = f(x, parameters)` to data.",
     "categories": [
-        "cubes",
+        "arrays",
         "math"
     ],
     "experimental": true,
     "parameters": [
         {
             "name": "data",
-            "description": "A data cube.",
+            "description": "A labeled array, the labels correspond to the variable `y` and the values correspond to the variable `x`.",
             "schema": {
-                "type": "object",
-                "subtype": "datacube"
+                "type": "array",
+                "subtype": "labeled-array",
+                "items": {
+                    "type": "number"
+                }
             }
         },
         {
             "name": "parameters",
             "description": "Defined the number of parameters for the model function and provides an initial guess for them. At least one parameter is required.",
-            "schema": [
-                {
-                    "type": "array",
-                    "minItems": 1,
-                    "items": {
-                        "type": "number"
-                    }
-                },
-                {
-                    "title": "Data Cube with optimal values from a previous result of this process.",
-                    "type": "object",
-                    "subtype": "datacube"
+            "schema": {
+                "type": "array",
+                "minItems": 1,
+                "items": {
+                    "type": "number"
                 }
-            ]
+            }
         },
         {
             "name": "function",
@@ -45,7 +41,10 @@
                         "name": "x",
                         "description": "The value for the independent variable `x`.",
                         "schema": {
-                            "type": "number"
+                            "type": [
+                                "number",
+                                "null"
+                            ]
                         }
                     },
                     {
@@ -69,26 +68,23 @@
             }
         },
         {
-            "name": "dimension",
-            "description": "The name of the dimension for curve fitting. Must be a dimension with labels that have a order (i.e. numerical labels or a temporal dimension). Fails with a `DimensionNotAvailable` exception if the specified dimension does not exist.",
+            "name": "ignore_nodata",
+            "description": "Indicates whether no-data values are ignored or not. Ignores them by default. Setting this flag to `false` considers no-data values so that `null` is passed to the model function.",
             "schema": {
-                "type": "string"
-            }
+                "type": "boolean"
+            },
+            "default": true,
+            "optional": true
         }
     ],
     "returns": {
-        "description": "A data cube with the optimal values for the parameters.",
+        "description": "An array with the optimal values for the parameters.",
         "schema": {
-            "type": "object",
-            "subtype": "datacube"
-        }
-    },
-    "exceptions": {
-        "InvalidValues": {
-            "message": "At least one of the values is not a finite number."
-        },
-        "DimensionNotAvailable": {
-            "message": "A dimension with the specified name does not exist."
+            "type": "array",
+            "minItems": 1,
+            "items": {
+                "type": "number"
+            }
         }
     }
 }
diff --git a/proposals/predict_curve.json b/proposals/predict_curve.json
index 9fb5d341..479b7fec 100644
--- a/proposals/predict_curve.json
+++ b/proposals/predict_curve.json
@@ -1,21 +1,13 @@
 {
     "id": "predict_curve",
     "summary": "Predict values",
-    "description": "Predict values using a model function and pre-computed parameters. The process is primarily intended to compute values for new labels, but it can also fill gaps where existing labels contain no-data (`null`) values.",
+    "description": "Predict values using a model function and pre-computed parameters. The process is intended to compute values for new labels.",
     "categories": [
         "cubes",
         "math"
     ],
     "experimental": true,
     "parameters": [
-        {
-            "name": "data",
-            "description": "A data cube to predict values for.",
-            "schema": {
-                "type": "object",
-                "subtype": "datacube"
-            }
-        },
         {
             "name": "parameters",
             "description": "A data cube with optimal values, e.g. computed by the process ``fit_curve()``.",
@@ -60,7 +52,7 @@
         },
         {
             "name": "dimension",
-            "description": "The name of the dimension for predictions. Fails with a `DimensionNotAvailable` exception if the specified dimension does not exist.",
+            "description": "The name of the dimension for predictions.",
             "schema": {
                 "type": "string"
             }
@@ -98,15 +90,10 @@
         }
     ],
     "returns": {
-        "description": "A data cube with the predicted values.",
+        "description": "A data cube with the predicted values with the provided dimension `dimension` having as many labels as provided through `labels`.",
         "schema": {
             "type": "object",
             "subtype": "datacube"
         }
-    },
-    "exceptions": {
-        "DimensionNotAvailable": {
-            "message": "A dimension with the specified name does not exist."
-        }
     }
 }