diff --git a/Lib/fontTools/varLib/__init__.py b/Lib/fontTools/varLib/__init__.py
index a106f2aff..2e87545d3 100644
--- a/Lib/fontTools/varLib/__init__.py
+++ b/Lib/fontTools/varLib/__init__.py
@@ -257,8 +257,8 @@ def _add_avar(font, axes, mappings, axisTags):
         varIdxes = {axis: optimized[value] for axis, value in varIdxes.items()}
 
         varIdxMap = ot.DeltaSetIndexMap()
-        varIdxMap.Format = 1
         varIdxMap.mapping = [varIdxes[t] for t in axisTags]
+        varIdxMap.Format = 1 if len(varIdxMap.mapping) > 0xFFFF else 0
 
         avar.majorVersion = 2
         avar.table = ot.avar()
diff --git a/Tests/varLib/data/BuildAvar2.designspace b/Tests/varLib/data/BuildAvar2.designspace
new file mode 100644
index 000000000..0a22fe6aa
--- /dev/null
+++ b/Tests/varLib/data/BuildAvar2.designspace
@@ -0,0 +1,62 @@
+<?xml version='1.0' encoding='utf-8'?>
+<designspace format="3">
+    <axes>
+        <axis default="400.0" maximum="900.0" minimum="100.0" name="weight" tag="wght">
+            <map input="100.0" output="26" />
+            <map input="200.0" output="39" />
+            <map input="300.0" output="58" />
+            <map input="400.0" output="90" />
+            <map input="500.0" output="108" />
+            <map input="600.0" output="128" />
+            <map input="700.0" output="151" />
+            <map input="800.0" output="169" />
+            <map input="900.0" output="190" />
+            <labelname xml:lang="en">Weight</labelname>
+        </axis>
+        <mappings>
+            <mapping>
+                <input>
+                    <dimension name="weight" xvalue="90"/>
+                </input>
+                <output>
+                </output>
+            </mapping>
+            <mapping>
+                <input>
+                    <dimension name="weight" xvalue="128"/>
+                </input>
+                <output>
+                    <dimension name="weight" xvalue="138"/>
+                </output>
+            </mapping>
+        </mappings>
+    </axes>
+    <sources>
+        <source familyname="Test Family 3" filename="master_ufo/TestFamily3-Light.ufo" name="Test Family 3 Light" stylename="Light">
+            <location>
+                <dimension name="weight" xvalue="26.000000" />
+            </location>
+        </source>
+        <source familyname="Test Family 3" filename="master_ufo/TestFamily3-Regular.ufo" name="Test Family 3 Regular" stylename="Regular">
+            <lib copy="1" />
+            <groups copy="1" />
+            <features copy="1" />
+            <info copy="1" />
+            <location>
+                <dimension name="weight" xvalue="90.000000" />
+            </location>
+        </source>
+        <source familyname="Test Family 3" filename="master_ufo/TestFamily3-SemiBold.ufo" name="Test Family 3 SemiBold" stylename="SemiBold">
+            <location>
+                <dimension name="weight" xvalue="151.000000" />
+            </location>
+        </source>
+        <source familyname="Test Family 3" filename="master_ufo/TestFamily3-Bold.ufo" name="Test Family 3 Bold" stylename="Bold">
+            <location>
+                <dimension name="weight" xvalue="190.000000" />
+            </location>
+        </source>
+    </sources>
+    <instances>
+    </instances>
+</designspace>
diff --git a/Tests/varLib/data/test_results/BuildAvar2.ttx b/Tests/varLib/data/test_results/BuildAvar2.ttx
new file mode 100644
index 000000000..1b16099c9
--- /dev/null
+++ b/Tests/varLib/data/test_results/BuildAvar2.ttx
@@ -0,0 +1,45 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<ttFont sfntVersion="\x00\x01\x00\x00" ttLibVersion="3.14">
+
+  <avar>
+    <version major="2" minor="0"/>
+    <segment axis="wght">
+      <mapping from="-1.0" to="-1.0"/>
+      <mapping from="-0.6667" to="-0.7969"/>
+      <mapping from="-0.3333" to="-0.5"/>
+      <mapping from="0.0" to="0.0"/>
+      <mapping from="0.2" to="0.18"/>
+      <mapping from="0.4" to="0.38"/>
+      <mapping from="0.6" to="0.61"/>
+      <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>
+        <!-- RegionAxisCount=1 -->
+        <!-- RegionCount=1 -->
+        <Region index="0">
+          <VarRegionAxis index="0">
+            <StartCoord value="0.0"/>
+            <PeakCoord value="0.38"/>
+            <EndCoord value="0.38"/>
+          </VarRegionAxis>
+        </Region>
+      </VarRegionList>
+      <!-- VarDataCount=1 -->
+      <VarData index="0">
+        <!-- ItemCount=1 -->
+        <NumShorts value="1"/>
+        <!-- VarRegionCount=1 -->
+        <VarRegionIndex index="0" value="0"/>
+        <Item index="0" value="[1638]"/>
+      </VarData>
+    </VarStore>
+  </avar>
+
+</ttFont>
diff --git a/Tests/varLib/varLib_test.py b/Tests/varLib/varLib_test.py
index a8f7a4574..cffd32f90 100644
--- a/Tests/varLib/varLib_test.py
+++ b/Tests/varLib/varLib_test.py
@@ -227,6 +227,19 @@ class BuildTest(unittest.TestCase):
             expected_ttx_name=test_name,
         )
 
+    def test_varlib_avar2(self):
+        """Designspace file contains a 'weight' axis with <map> elements
+        modifying the normalization mapping as well as <mappings> element
+        modifying it post-normalization. An 'avar' table is generated.
+        """
+        test_name = "BuildAvar2"
+        self._run_varlib_build_test(
+            designspace_name=test_name,
+            font_name="TestFamily3",
+            tables=["avar"],
+            expected_ttx_name=test_name,
+        )
+
     def test_varlib_build_feature_variations(self):
         """Designspace file contains <rules> element, used to build
         GSUB FeatureVariations table.
@@ -912,7 +925,6 @@ Expected: kern, mark.
 Got: kern.
 """,
         ):
-
             self._run_varlib_build_test(
                 designspace_name="IncompatibleFeatures",
                 font_name="IncompatibleFeatures",