diff --git a/src/spikeinterface/preprocessing/common_reference.py b/src/spikeinterface/preprocessing/common_reference.py
index 3b5faa1381..5231f8f6c8 100644
--- a/src/spikeinterface/preprocessing/common_reference.py
+++ b/src/spikeinterface/preprocessing/common_reference.py
@@ -8,6 +8,7 @@
 from spikeinterface.core.baserecording import BaseRecording
 
 from .filter import fix_dtype
+from functools import cache
 
 
 class CommonReferenceRecording(BasePreprocessor):
@@ -83,13 +84,14 @@ def __init__(
         groups: list | None = None,
         ref_channel_ids: list | str | int | None = None,
         local_radius: tuple[float, float] = (30.0, 55.0),
+        min_local_neighbors: int = 5,
         dtype: str | np.dtype | None = None,
     ):
         num_chans = recording.get_num_channels()
         neighbors = None
         # some checks
         if reference not in ("global", "single", "local"):
-            raise ValueError("'reference' must be either 'global', 'single' or 'local'")
+            raise ValueError("'reference' must be either 'global', 'single', 'local'")
         if operator not in ("median", "average"):
             raise ValueError("'operator' must be either 'median', 'average'")
 
@@ -117,10 +119,10 @@ def __init__(
             closest_inds, dist = get_closest_channels(recording)
             neighbors = {}
             for i in range(num_chans):
-                mask = (dist[i, :] > local_radius[0]) & (dist[i, :] <= local_radius[1])
+                mask = dist[i, :] > local_radius[0]
+                nn = np.cumsum(mask)
+                mask &= (dist[i, :] <= local_radius[1]) | ((0 < nn) & (nn <= min_local_neighbors))
                 neighbors[i] = closest_inds[i, mask]
-                assert len(neighbors[i]) > 0, "No reference channels available in the local annulus for selection."
-
         dtype_ = fix_dtype(recording, dtype)
         BasePreprocessor.__init__(self, recording, dtype=dtype_)
 
@@ -136,7 +138,14 @@ def __init__(
 
         for parent_segment in recording._recording_segments:
             rec_segment = CommonReferenceRecordingSegment(
-                parent_segment, reference, operator, group_indices, ref_channel_indices, local_radius, neighbors, dtype_
+                parent_segment,
+                reference,
+                operator,
+                group_indices,
+                ref_channel_indices,
+                local_radius,
+                neighbors,
+                dtype_,
             )
             self.add_recording_segment(rec_segment)
 
@@ -147,6 +156,7 @@ def __init__(
             operator=operator,
             ref_channel_ids=ref_channel_ids,
             local_radius=local_radius,
+            min_local_neighbors=min_local_neighbors,
             dtype=dtype_.str,
         )