diff --git a/distributed/shuffle/__init__.py b/distributed/shuffle/__init__.py
index 2a073116781..64c7fe012b4 100644
--- a/distributed/shuffle/__init__.py
+++ b/distributed/shuffle/__init__.py
@@ -1,8 +1,14 @@
 from __future__ import annotations
 
-from distributed.shuffle.shuffle import rearrange_by_column_p2p
-from distributed.shuffle.shuffle_extension import (
-    ShuffleId,
+from distributed.shuffle._shuffle import P2PShuffleLayer, rearrange_by_column_p2p
+from distributed.shuffle._shuffle_extension import (
     ShuffleSchedulerExtension,
     ShuffleWorkerExtension,
 )
+
+__all__ = [
+    "P2PShuffleLayer",
+    "rearrange_by_column_p2p",
+    "ShuffleSchedulerExtension",
+    "ShuffleWorkerExtension",
+]
diff --git a/distributed/shuffle/arrow.py b/distributed/shuffle/_arrow.py
similarity index 100%
rename from distributed/shuffle/arrow.py
rename to distributed/shuffle/_arrow.py
diff --git a/distributed/shuffle/multi_comm.py b/distributed/shuffle/_multi_comm.py
similarity index 100%
rename from distributed/shuffle/multi_comm.py
rename to distributed/shuffle/_multi_comm.py
diff --git a/distributed/shuffle/multi_file.py b/distributed/shuffle/_multi_file.py
similarity index 100%
rename from distributed/shuffle/multi_file.py
rename to distributed/shuffle/_multi_file.py
diff --git a/distributed/shuffle/shuffle.py b/distributed/shuffle/_shuffle.py
similarity index 91%
rename from distributed/shuffle/shuffle.py
rename to distributed/shuffle/_shuffle.py
index ca3fe0c3c0d..df5f0c6b712 100644
--- a/distributed/shuffle/shuffle.py
+++ b/distributed/shuffle/_shuffle.py
@@ -6,7 +6,7 @@
 from dask.highlevelgraph import HighLevelGraph
 from dask.layers import SimpleShuffleLayer
 
-from distributed.shuffle.shuffle_extension import ShuffleId, ShuffleWorkerExtension
+from distributed.shuffle._shuffle_extension import ShuffleId, ShuffleWorkerExtension
 
 if TYPE_CHECKING:
     import pandas as pd
@@ -14,7 +14,7 @@
     from dask.dataframe import DataFrame
 
 
-def get_ext() -> ShuffleWorkerExtension:
+def _get_worker_extension() -> ShuffleWorkerExtension:
     from distributed import get_worker
 
     try:
@@ -25,7 +25,7 @@ def get_ext() -> ShuffleWorkerExtension:
             "please confirm that you've created a distributed Client and are submitting this computation through it."
         ) from e
     extension: ShuffleWorkerExtension | None = worker.extensions.get("shuffle")
-    if not extension:
+    if extension is None:
         raise RuntimeError(
             f"The worker {worker.address} does not have a ShuffleExtension. "
             "Is pandas installed on the worker?"
@@ -39,17 +39,19 @@ def shuffle_transfer(
     npartitions: int,
     column: str,
 ) -> None:
-    get_ext().add_partition(input, id, npartitions=npartitions, column=column)
+    _get_worker_extension().add_partition(
+        input, id, npartitions=npartitions, column=column
+    )
 
 
 def shuffle_unpack(
     id: ShuffleId, output_partition: int, barrier: object
 ) -> pd.DataFrame:
-    return get_ext().get_output_partition(id, output_partition)
+    return _get_worker_extension().get_output_partition(id, output_partition)
 
 
 def shuffle_barrier(id: ShuffleId, transfers: list[None]) -> None:
-    get_ext().barrier(id)
+    return _get_worker_extension().barrier(id)
 
 
 def rearrange_by_column_p2p(
diff --git a/distributed/shuffle/shuffle_extension.py b/distributed/shuffle/_shuffle_extension.py
similarity index 98%
rename from distributed/shuffle/shuffle_extension.py
rename to distributed/shuffle/_shuffle_extension.py
index bad94aeee95..ded1d84c985 100644
--- a/distributed/shuffle/shuffle_extension.py
+++ b/distributed/shuffle/_shuffle_extension.py
@@ -13,14 +13,14 @@
 import toolz
 
 from distributed.protocol import to_serialize
-from distributed.shuffle.arrow import (
+from distributed.shuffle._arrow import (
     deserialize_schema,
     dump_batch,
     list_of_buffers_to_table,
     load_arrow,
 )
-from distributed.shuffle.multi_comm import MultiComm
-from distributed.shuffle.multi_file import MultiFile
+from distributed.shuffle._multi_comm import MultiComm
+from distributed.shuffle._multi_file import MultiFile
 from distributed.utils import log_errors, sync
 
 if TYPE_CHECKING:
@@ -559,7 +559,9 @@ def split_by_worker(
     if not nrows:
         return {}
     # assert len(df) == nrows  # Not true if some outputs aren't wanted
-    t = pa.Table.from_pandas(df)
+    # FIXME: If we do not preserve the index something is corrupting the
+    # bytestream such that it cannot be deserialized anymore
+    t = pa.Table.from_pandas(df, preserve_index=True)
     t = t.sort_by("_worker")
     codes = np.asarray(t.select(["_worker"]))[0]
     t = t.drop(["_worker"])
diff --git a/distributed/shuffle/tests/test_graph.py b/distributed/shuffle/tests/test_graph.py
index 028b955aa5e..ffa84553110 100644
--- a/distributed/shuffle/tests/test_graph.py
+++ b/distributed/shuffle/tests/test_graph.py
@@ -13,7 +13,7 @@
 from dask.blockwise import Blockwise
 from dask.utils_test import hlg_layer_topological
 
-from distributed.shuffle.shuffle_extension import ShuffleWorkerExtension
+from distributed.shuffle._shuffle_extension import ShuffleWorkerExtension
 from distributed.utils_test import gen_cluster
 
 
diff --git a/distributed/shuffle/tests/test_multi_comm.py b/distributed/shuffle/tests/test_multi_comm.py
index d45a4d18b93..90919511701 100644
--- a/distributed/shuffle/tests/test_multi_comm.py
+++ b/distributed/shuffle/tests/test_multi_comm.py
@@ -5,7 +5,7 @@
 
 import pytest
 
-from distributed.shuffle.multi_comm import MultiComm
+from distributed.shuffle._multi_comm import MultiComm
 from distributed.utils_test import gen_test
 
 
diff --git a/distributed/shuffle/tests/test_multi_file.py b/distributed/shuffle/tests/test_multi_file.py
index 16ebc7562c9..9dddd3cd3a7 100644
--- a/distributed/shuffle/tests/test_multi_file.py
+++ b/distributed/shuffle/tests/test_multi_file.py
@@ -5,7 +5,7 @@
 
 import pytest
 
-from distributed.shuffle.multi_file import MultiFile
+from distributed.shuffle._multi_file import MultiFile
 from distributed.utils_test import gen_test
 
 
diff --git a/distributed/shuffle/tests/test_shuffle.py b/distributed/shuffle/tests/test_shuffle.py
index 63e245bb23d..5d15f68ffc6 100644
--- a/distributed/shuffle/tests/test_shuffle.py
+++ b/distributed/shuffle/tests/test_shuffle.py
@@ -17,7 +17,7 @@
 from dask.distributed import Worker
 from dask.utils import stringify
 
-from distributed.shuffle.shuffle_extension import (
+from distributed.shuffle._shuffle_extension import (
     dump_batch,
     list_of_buffers_to_table,
     load_arrow,
diff --git a/distributed/shuffle/tests/test_shuffle_extension.py b/distributed/shuffle/tests/test_shuffle_extension.py
index b3ffbcc6988..78b6e3b64fd 100644
--- a/distributed/shuffle/tests/test_shuffle_extension.py
+++ b/distributed/shuffle/tests/test_shuffle_extension.py
@@ -5,7 +5,7 @@
 pd = pytest.importorskip("pandas")
 dd = pytest.importorskip("dask.dataframe")
 
-from distributed.shuffle.shuffle_extension import (
+from distributed.shuffle._shuffle_extension import (
     ShuffleWorkerExtension,
     get_worker_for,
     split_by_partition,
@@ -22,7 +22,6 @@ async def test_installation(s, a):
     assert a.handlers["shuffle_inputs_done"] == ext.shuffle_inputs_done
 
 
-@pytest.mark.skip
 def test_split_by_worker():
     df = pd.DataFrame(
         {
@@ -30,17 +29,32 @@ def test_split_by_worker():
             "_partition": [0, 1, 2, 0, 1],
         }
     )
+
     workers = ["alice", "bob"]
+    worker_for_mapping = {}
     npartitions = 3
-
-    out = split_by_worker(df, "_partition", npartitions, workers)
+    for part in range(npartitions):
+        worker_for_mapping[part] = get_worker_for(part, workers, npartitions)
+    worker_for = pd.Series(worker_for_mapping, name="_workers").astype("category")
+    out = split_by_worker(df, "_partition", worker_for)
     assert set(out) == {"alice", "bob"}
-    assert out["alice"].column_names == list(df.columns)
+    assert list(out["alice"].to_pandas().columns) == list(df.columns)
 
     assert sum(map(len, out.values())) == len(df)
 
 
-@pytest.mark.skip
+def test_split_by_worker_empty():
+    df = pd.DataFrame(
+        {
+            "x": [1, 2, 3, 4, 5],
+            "_partition": [0, 1, 2, 0, 1],
+        }
+    )
+    worker_for = pd.Series({5: "chuck"}, name="_workers").astype("category")
+    out = split_by_worker(df, "_partition", worker_for)
+    assert out == {}
+
+
 def test_split_by_worker_many_workers():
     df = pd.DataFrame(
         {
@@ -50,8 +64,11 @@ def test_split_by_worker_many_workers():
     )
     workers = ["a", "b", "c", "d", "e", "f", "g", "h"]
     npartitions = 10
-
-    out = split_by_worker(df, "_partition", npartitions, workers)
+    worker_for_mapping = {}
+    for part in range(npartitions):
+        worker_for_mapping[part] = get_worker_for(part, workers, npartitions)
+    worker_for = pd.Series(worker_for_mapping, name="_workers").astype("category")
+    out = split_by_worker(df, "_partition", worker_for)
     assert get_worker_for(5, workers, npartitions) in out
     assert get_worker_for(0, workers, npartitions) in out
     assert get_worker_for(7, workers, npartitions) in out