diff --git a/src/spikeinterface/preprocessing/common_reference.py b/src/spikeinterface/preprocessing/common_reference.py
index a4369309f2..ffe7467753 100644
--- a/src/spikeinterface/preprocessing/common_reference.py
+++ b/src/spikeinterface/preprocessing/common_reference.py
@@ -39,7 +39,8 @@ class CommonReferenceRecording(BasePreprocessor):
     recording: RecordingExtractor
         The recording extractor to be re-referenced
     reference: "global" | "single" | "local", default: "global"
-        If "global" the reference is the average or median across all the channels.
+        If "global" the reference is the average or median across all the channels. To select a subset of channels,
+        you can use the `ref_channel_ids` parameter.
         If "single", the reference is a single channel or a list of channels that need to be set with the `ref_channel_ids`.
         If "local", the reference is the set of channels within an annulus that must be set with the `local_radius` parameter.
     operator: "median" | "average", default: "median"
@@ -51,11 +52,11 @@ class CommonReferenceRecording(BasePreprocessor):
         List of lists containing the channel ids for splitting the reference. The CMR, CAR, or referencing with respect to
         single channels are applied group-wise. However, this is not applied for the local CAR.
         It is useful when dealing with different channel groups, e.g. multiple tetrodes.
-    ref_channel_ids: list or str or int, default: None
-        If no "groups" are specified, all channels are referenced to "ref_channel_ids". If "groups" is provided, then a
-        list of channels to be applied to each group is expected. If "single" reference, a list of one channel or an
-        int is expected.
-    local_radius: tuple(int, int), default: (30, 55)
+    ref_channel_ids: list | str | int | None, default: None
+        If "global" reference, a list of channels to be used as reference.
+        If "single" reference, a list of one channel or a single channel id is expected.
+        If "groups" is provided, then a list of channels to be applied to each group is expected.
+    local_radius : tuple(int, int), default: (30, 55)
         Use in the local CAR implementation as the selecting annulus with the following format:
 
         `(exclude radius, include radius)`
@@ -82,10 +83,10 @@ def __init__(
         recording: BaseRecording,
         reference: Literal["global", "single", "local"] = "global",
         operator: Literal["median", "average"] = "median",
-        groups=None,
-        ref_channel_ids=None,
-        local_radius=(30, 55),
-        dtype=None,
+        groups: list | None = None,
+        ref_channel_ids: list | str | int | None = None,
+        local_radius: tuple[float, float] = (30.0, 55.0),
+        dtype: str | np.dtype | None = None,
     ):
         num_chans = recording.get_num_channels()
         neighbors = None
@@ -96,7 +97,9 @@ def __init__(
             raise ValueError("'operator' must be either 'median', 'average'")
 
         if reference == "global":
-            pass
+            if ref_channel_ids is not None:
+                if not isinstance(ref_channel_ids, list):
+                    raise ValueError("With 'global' reference, provide 'ref_channel_ids' as a list")
         elif reference == "single":
             assert ref_channel_ids is not None, "With 'single' reference, provide 'ref_channel_ids'"
             if groups is not None:
@@ -182,7 +185,10 @@ def get_traces(self, start_frame, end_frame, channel_indices):
             traces = self.parent_recording_segment.get_traces(start_frame, end_frame, slice(None))
 
             if self.reference == "global":
-                shift = self.operator_func(traces, axis=1, keepdims=True)
+                if self.ref_channel_indices is None:
+                    shift = self.operator_func(traces, axis=1, keepdims=True)
+                else:
+                    shift = self.operator_func(traces[:, self.ref_channel_indices], axis=1, keepdims=True)
                 re_referenced_traces = traces[:, channel_indices] - shift
             elif self.reference == "single":
                 # single channel -> no need of operator
diff --git a/src/spikeinterface/preprocessing/tests/test_common_reference.py b/src/spikeinterface/preprocessing/tests/test_common_reference.py
index 1df9b21c81..8b37e7f4b9 100644
--- a/src/spikeinterface/preprocessing/tests/test_common_reference.py
+++ b/src/spikeinterface/preprocessing/tests/test_common_reference.py
@@ -11,7 +11,7 @@
 
 def _generate_test_recording():
     recording = generate_recording(durations=[1.0], num_channels=4)
-    recording = recording.channel_slice(recording.channel_ids, np.array(["a", "b", "c", "d"]))
+    recording = recording.rename_channels(np.array(["a", "b", "c", "d"]))
     return recording
 
 
@@ -23,12 +23,14 @@ def recording():
 def test_common_reference(recording):
     # Test simple case
     rec_cmr = common_reference(recording, reference="global", operator="median")
+    rec_cmr_ref = common_reference(recording, reference="global", operator="median", ref_channel_ids=["a", "b", "c"])
     rec_car = common_reference(recording, reference="global", operator="average")
     rec_sin = common_reference(recording, reference="single", ref_channel_ids=["a"])
     rec_local_car = common_reference(recording, reference="local", local_radius=(20, 65), operator="median")
 
     traces = recording.get_traces()
     assert np.allclose(traces, rec_cmr.get_traces() + np.median(traces, axis=1, keepdims=True), atol=0.01)
+    assert np.allclose(traces, rec_cmr_ref.get_traces() + np.median(traces[:, :3], axis=1, keepdims=True), atol=0.01)
     assert np.allclose(traces, rec_car.get_traces() + np.mean(traces, axis=1, keepdims=True), atol=0.01)
     assert not np.all(rec_sin.get_traces()[0])
     assert np.allclose(rec_sin.get_traces()[:, 1], traces[:, 1] - traces[:, 0])