diff --git a/Lib/fontTools/ttLib/tables/otTables.py b/Lib/fontTools/ttLib/tables/otTables.py
index 237864bb2..97a4487a7 100644
--- a/Lib/fontTools/ttLib/tables/otTables.py
+++ b/Lib/fontTools/ttLib/tables/otTables.py
@@ -546,21 +546,26 @@ class VarIdxMap(BaseTable):
 
 	def populateDefaults(self, propagator=None):
 		if not hasattr(self, 'mapping'):
-			self.mapping = []
+			self.mapping = {}
 
 	def postRead(self, rawTable, font):
 		assert (rawTable['EntryFormat'] & 0xFFC0) == 0
-		self.mapping = rawTable['mapping']
+		glyphOrder = font.getGlyphOrder()
+		mapList = rawTable['mapping']
+		mapList.extend([mapList[-1]] * (len(glyphOrder) - len(mapList)))
+		self.mapping = dict(zip(glyphOrder, mapList))
 
 	def preWrite(self, font):
 		mapping = getattr(self, "mapping", None)
 		if mapping is None:
-			mapping = self.mapping = []
+			mapping = self.mapping = {}
+
+		glyphOrder = font.getGlyphOrder()
+		mapping = [mapping[g] for g in glyphOrder]
+
 		rawTable = { 'mapping': mapping }
 		rawTable['MappingCount'] = len(mapping)
 
-		# TODO Remove this abstraction/optimization and move it varLib.builder?
-
 		ored = 0
 		for idx in mapping:
 			ored |= idx
@@ -589,9 +594,9 @@ class VarIdxMap(BaseTable):
 		return rawTable
 
 	def toXML2(self, xmlWriter, font):
-		for i, value in enumerate(getattr(self, "mapping", [])):
+		for glyph, value in sorted(getattr(self, "mapping", {}).items()):
 			attrs = (
-				('index', i),
+				('glyph', glyph),
 				('outer', value >> 16),
 				('inner', value & 0xFFFF),
 			)
@@ -601,12 +606,13 @@ class VarIdxMap(BaseTable):
 	def fromXML(self, name, attrs, content, font):
 		mapping = getattr(self, "mapping", None)
 		if mapping is None:
-			mapping = []
+			mapping = {}
 			self.mapping = mapping
+		glyph = attrs['glyph']
 		outer = safeEval(attrs['outer'])
 		inner = safeEval(attrs['inner'])
 		assert inner <= 0xFFFF
-		mapping.append((outer << 16) | inner)
+		mapping[glyph] = (outer << 16) | inner
 
 
 class SingleSubst(FormatSwitchingBaseTable):
diff --git a/Lib/fontTools/varLib/__init__.py b/Lib/fontTools/varLib/__init__.py
index d622d21d4..47d266a5a 100644
--- a/Lib/fontTools/varLib/__init__.py
+++ b/Lib/fontTools/varLib/__init__.py
@@ -436,9 +436,7 @@ def _add_HVAR(font, model, master_ttfs, axisTags):
 		newItems = sorted(uniq)
 		mapper = {v:i for i,v in enumerate(newItems)}
 		mapping = [mapper[item] for item in items]
-		while len(mapping) > 1 and mapping[-1] == mapping[-2]:
-			del mapping[-1]
-		advanceMapping = builder.buildVarIdxMap(mapping)
+		advanceMapping = builder.buildVarIdxMap(mapping, font.getGlyphOrder())
 		items = newItems
 		del mapper, mapping, newItems
 	del uniq
diff --git a/Lib/fontTools/varLib/builder.py b/Lib/fontTools/varLib/builder.py
index 9f73ea01b..887e4fb75 100644
--- a/Lib/fontTools/varLib/builder.py
+++ b/Lib/fontTools/varLib/builder.py
@@ -84,10 +84,9 @@ def buildVarStore(varRegionList, varDataList):
 
 # Variation helpers
 
-def buildVarIdxMap(varIdxes):
-	# TODO Change VarIdxMap mapping to hold separate outer,inner indices
+def buildVarIdxMap(varIdxes, glyphOrder):
 	self = ot.VarIdxMap()
-	self.mapping = list(varIdxes)
+	self.mapping = {g:v for g,v in zip(glyphOrder, varIdxes)}
 	return self
 
 def buildVarDevTable(varIdx):
diff --git a/Tests/varLib/data/master_ttx_varfont_ttf/Mutator_IUP.ttx b/Tests/varLib/data/master_ttx_varfont_ttf/Mutator_IUP.ttx
index 8cbd8a69c..23c240eff 100755
--- a/Tests/varLib/data/master_ttx_varfont_ttf/Mutator_IUP.ttx
+++ b/Tests/varLib/data/master_ttx_varfont_ttf/Mutator_IUP.ttx
@@ -405,11 +405,13 @@
       </VarData>
     </VarStore>
     <AdvWidthMap>
-      <Map index="0" outer="0" inner="1"/>
-      <Map index="1" outer="0" inner="1"/>
-      <Map index="2" outer="0" inner="1"/>
-      <Map index="3" outer="0" inner="1"/>
-      <Map index="4" outer="0" inner="0"/>
+      <Map glyph=".notdef" outer="0" inner="1"/>
+      <Map glyph="NULL" outer="0" inner="1"/>
+      <Map glyph="a" outer="0" inner="0"/>
+      <Map glyph="b" outer="0" inner="0"/>
+      <Map glyph="q" outer="0" inner="0"/>
+      <Map glyph="nonmarkingreturn" outer="0" inner="1"/>
+      <Map glyph="space" outer="0" inner="1"/>
     </AdvWidthMap>
   </HVAR>