diff --git a/python/rascaline/rascaline/utils/clebsch_gordan/_cg_product.py b/python/rascaline/rascaline/utils/clebsch_gordan/_cg_product.py
index 6bb47c6de..6e5268752 100644
--- a/python/rascaline/rascaline/utils/clebsch_gordan/_cg_product.py
+++ b/python/rascaline/rascaline/utils/clebsch_gordan/_cg_product.py
@@ -300,10 +300,10 @@ def _cg_tensor_product(
 
         # 3. a) Apply key selections
         if selected_keys is not None:
-            output_keys, combinations = _utils._apply_key_selection(
-                output_keys,
-                combinations,
-                selected_keys,
+            selected_idx = output_keys.select(selected_keys)
+            combinations = [combinations[i] for i in selected_idx]
+            output_keys = Labels(
+                names=output_keys.names, values=output_keys.values[selected_idx]
             )
 
         # 3. b) Apply key filter
diff --git a/python/rascaline/rascaline/utils/clebsch_gordan/_utils.py b/python/rascaline/rascaline/utils/clebsch_gordan/_utils.py
index 01505650e..b02292d3d 100644
--- a/python/rascaline/rascaline/utils/clebsch_gordan/_utils.py
+++ b/python/rascaline/rascaline/utils/clebsch_gordan/_utils.py
@@ -160,62 +160,6 @@ def _compute_output_keys(
     return output_keys, combinations
 
 
-def _apply_key_selection(
-    output_keys: Labels,
-    combinations: List[Tuple[int, int]],
-    selected_keys: Labels,
-) -> Tuple[Labels, List[Tuple[int, int]]]:
-    """
-    Applies a selection according to ``selected_keys`` to the keys of an output
-    TensorMap ``output_keys`` produced by the provided ``combinations`` of blocks.
-
-    After application of the selections, returned is a reduced set of keys and set of
-    corresponding parents key entries.
-
-    If a selection in ``selected_keys`` is not valid based on the keys in
-    ``output_keys``, we raise an error.
-    """
-    # Extract the relevant columns from `selected_keys` that the selection will be
-    # performed on
-    col_idx = _dispatch.int_array_like(
-        [output_keys.names.index(name) for name in selected_keys.names],
-        output_keys.values,
-    )
-    output_keys_values = output_keys.values[:, col_idx]
-
-    # First check that all of the selected keys exist in the output keys
-    for selected in selected_keys.values:
-        if not any(
-            [
-                bool(all(selected == output_keys_values[i]))
-                for i in range(len(output_keys_values))
-            ]
-        ):
-            raise ValueError(
-                f"selected key {selected_keys.names} = {selected} not found "
-                "in the output keys"
-            )
-
-    # Build a mask of the selected keys
-    mask = _dispatch.bool_array_like(
-        [
-            any([bool(all(i == j)) for j in selected_keys.values])
-            for i in output_keys_values
-        ],
-        like=selected_keys.values,
-    )
-
-    mask_indices = _dispatch.int_array_like(
-        list(range(len(combinations))), like=selected_keys.values
-    )[mask]
-
-    # Apply the mask to combinations and keys
-    combinations = [combinations[i] for i in mask_indices]
-    output_keys = Labels(names=output_keys.names, values=output_keys.values[mask])
-
-    return output_keys, combinations
-
-
 def _group_combinations_of_same_blocks(
     output_keys: Labels,
     combinations: List[Tuple[int, int]],