diff --git a/esmvalcore/cmor/table.py b/esmvalcore/cmor/table.py
index 0f6c5d680e..067d4f9da8 100644
--- a/esmvalcore/cmor/table.py
+++ b/esmvalcore/cmor/table.py
@@ -164,11 +164,7 @@ def _assign_dimensions(self, var, generic_levels):
                     )
                     raise
 
-            axis = coord.axis
-            if not axis:
-                axis = 'none'
-
-            var.coordinates[axis] = coord
+            var.coordinates[dimension] = coord
 
     def _load_coordinates(self):
         self.coords = {}
@@ -392,7 +388,11 @@ def __init__(self, table_type, short_name):
         self.dimensions = []
         """List of dimensions"""
         self.coordinates = {}
-        """Coordinates"""
+        """Coordinates
+
+        This is a dict with the names of the dimensions as keys and
+        CoordinateInfo objects as values.
+        """
 
         self._json_data = None