diff --git a/Lib/fontTools/varLib/__init__.py b/Lib/fontTools/varLib/__init__.py
index 0320ef073..565e01b3a 100644
--- a/Lib/fontTools/varLib/__init__.py
+++ b/Lib/fontTools/varLib/__init__.py
@@ -264,6 +264,8 @@ def _add_avar(font, axes, mappings, axisTags):
         varIdxMap = ot.DeltaSetIndexMap()
         varIdxMap.mapping = [varIdxes[t] for t in axisTags]
         varIdxMap.Format = 1 if len(varIdxMap.mapping) > 0xFFFF else 0
+        if all(i == v for i, v in enumerate(varIdxMap.mapping)):
+            varIdxMap = None
 
         avar.majorVersion = 2
         avar.table = ot.avar()
diff --git a/Tests/varLib/data/test_results/BuildAvar2.ttx b/Tests/varLib/data/test_results/BuildAvar2.ttx
index 1b16099c9..27a41bfbb 100644
--- a/Tests/varLib/data/test_results/BuildAvar2.ttx
+++ b/Tests/varLib/data/test_results/BuildAvar2.ttx
@@ -14,10 +14,6 @@
       <mapping from="0.8" to="0.79"/>
       <mapping from="1.0" to="1.0"/>
     </segment>
-    <VarIdxMap Format="0">
-      <!-- Omitted values default to 0xFFFF/0xFFFF (no variations) -->
-      <Map index="0" outer="0" inner="0"/>
-    </VarIdxMap>
     <VarStore Format="1">
       <Format value="1"/>
       <VarRegionList>