diff --git a/odc/geo/crs.py b/odc/geo/crs.py
index 6c208aa..42e002a 100644
--- a/odc/geo/crs.py
+++ b/odc/geo/crs.py
@@ -213,8 +213,15 @@ class CRS:
             return "degrees_north", "degrees_east"
 
         if self.projected:
-            x, y = self._crs.axis_info
-            return x.unit_name, y.unit_name
+            # Handle compound CRS by taking the first two spatial axes (typically easting, northing)
+            axis_info = self._crs.axis_info
+            if len(axis_info) >= 2:
+                # Take the first two axes which should be the spatial dimensions
+                x, y = axis_info[0], axis_info[1]
+                return x.unit_name, y.unit_name
+            else:
+                # Fallback for unexpected cases
+                raise ValueError("Expected at least 2 axes in projected CRS")
 
         raise ValueError("Neither projected nor geographic")  # pragma: no cover