diff --git a/odc/stats/plugins/gm.py b/odc/stats/plugins/gm.py
index 30981a67..f4f27e9b 100644
--- a/odc/stats/plugins/gm.py
+++ b/odc/stats/plugins/gm.py
@@ -5,7 +5,7 @@
 import xarray as xr
 from odc.algo import geomedian_with_mads
 from ._registry import StatsPluginInterface, register
-from odc.algo import enum_to_bool, erase_bad
+from odc.algo import enum_to_bool, erase_bad, keep_good_only
 from odc.algo import mask_cleanup
 import logging
 
@@ -104,7 +104,14 @@ def native_transform(self, xx: xr.Dataset) -> xr.Dataset:
             xx = xx.drop_vars([self._mask_band] + [self._contiguity_band])
         else:
             xx = xx.drop_vars([self._mask_band])
+
         xx = erase_bad(xx, bad)
+
+        # Remove sentinel-2 pixels valued 1 (scene edges, terrain shadow)
+        if self._mask_band == "SCL":
+            valid_data_mask = (xx > 1).to_array(dim="band").all(dim="band")
+            xx = keep_good_only(xx, where=valid_data_mask)
+
         return xx
 
     def reduce(self, xx: xr.Dataset) -> xr.Dataset: