diff --git a/Lib/fontTools/fontBuilder.py b/Lib/fontTools/fontBuilder.py
index d4b940512..f3fe92a83 100644
--- a/Lib/fontTools/fontBuilder.py
+++ b/Lib/fontTools/fontBuilder.py
@@ -803,6 +803,15 @@ class FontBuilder(object):
             nameTable=self.font.get("name")
         )
 
+    def setupStat(self, axes, locations=None, elidedFallbackName=2):
+        """Build a new 'STAT' table.
+
+        See `fontTools.otlLib.builder.buildStatTable` for details about
+        the arguments.
+        """
+        from .otlLib.builder import buildStatTable
+        buildStatTable(self.font, axes, locations, elidedFallbackName)
+
 
 def buildCmapSubTable(cmapping, format, platformID, platEncID):
     subTable = cmap_classes[format](format)
diff --git a/Lib/fontTools/otlLib/builder.py b/Lib/fontTools/otlLib/builder.py
index dd0aabe75..4d9d2bc02 100644
--- a/Lib/fontTools/otlLib/builder.py
+++ b/Lib/fontTools/otlLib/builder.py
@@ -1,4 +1,5 @@
 from collections import namedtuple
+from fontTools.misc.fixedTools import fixedToFloat
 from fontTools import ttLib
 from fontTools.ttLib.tables import otTables as ot
 from fontTools.ttLib.tables.otBase import ValueRecord, valueRecordFormatDict
@@ -657,3 +658,193 @@ class ClassDefBuilder(object):
         classDef = ot.ClassDef()
         classDef.classDefs = glyphClasses
         return classDef
+
+
+AXIS_VALUE_NEGATIVE_INFINITY = fixedToFloat(-0x80000000, 16)
+AXIS_VALUE_POSITIVE_INFINITY = fixedToFloat(0x7FFFFFFF, 16)
+
+
+def buildStatTable(ttFont, axes, locations=None, elidedFallbackName=2):
+    """Add a 'STAT' table to 'ttFont'.
+
+    'axes' is a list of dictionaries describing axes and their
+    values.
+
+    Example:
+
+    axes = [
+        dict(
+            tag="wght",
+            name="Weight",
+            ordering=0,  # optional
+            values=[
+                dict(value=100, name='Thin'),
+                dict(value=300, name='Light'),
+                dict(value=400, name='Regular', flags=0x2),
+                dict(value=900, name='Black'),
+            ],
+        )
+    ]
+
+    Each axis dict must have 'tag' and 'name' items. 'tag' maps
+    to the 'AxisTag' field. 'name' can be a name ID (int), a string,
+    or a dictionary containing multilingual names (see the
+    addMultilingualName() name table method), and will translate to
+    the AxisNameID field.
+
+    An axis dict may contain an 'ordering' item that maps to the
+    AxisOrdering field. If omitted, the order of the axes list is
+    used to calculate AxisOrdering fields.
+
+    The axis dict may contain a 'values' item, which is a list of
+    dictionaries describing AxisValue records belonging to this axis.
+
+    Each value dict must have a 'name' item, which can be a name ID
+    (int), a string, or a dictionary containing multilingual names,
+    like the axis name. It translates to the ValueNameID field.
+
+    Optionally the value dict can contain a 'flags' item. It maps to
+    the AxisValue Flags field, and will be 0 when omitted.
+
+    The format of the AxisValue is determined by the remaining contents
+    of the value dictionary:
+
+    If the value dict contains a 'value' item, an AxisValue record
+    Format 1 is created. If in addition to the 'value' item it contains
+    a 'linkedValue' item, an AxisValue record Format 3 is built.
+
+    If the value dict contains a 'nominalValue' item, an AxisValue
+    record Format 2 is built. Optionally it may contain 'rangeMinValue'
+    and 'rangeMaxValue' items. These map to -Infinity and +Infinity
+    respectively if omitted.
+
+    You cannot specify Format 4 AxisValue tables this way, as they are
+    not tied to a single axis, and specify a name for a location that
+    is defined by multiple axes values. Instead, you need to supply the
+    'locations' argument.
+
+    The optional 'locations' argument specifies AxisValue Format 4
+    tables. It should be a list of dicts, where each dict has a 'name'
+    item, which works just like the value dicts above, an optional
+    'flags' item (defaulting to 0x0), and a 'location' dict. A
+    location dict key is an axis tag, and the associated value is the
+    location on the specified axis. They map to the AxisIndex and Value
+    fields of the AxisValueRecord.
+
+    Example:
+
+    locations = [
+        dict(name='Regular ABCD', location=dict(wght=300, ABCD=100)),
+        dict(name='Bold ABCD XYZ', location=dict(wght=600, ABCD=200)),
+    ]
+
+    The optional 'elidedFallbackName' argument can be a name ID (int),
+    a string, or a dictionary containing multilingual names. It
+    translates to the ElidedFallbackNameID field.
+
+    The 'ttFont' argument must be a TTFont instance that already has a
+    'name' table. If a 'STAT' table already exists, it will be
+    overwritten by the newly created one.
+    """
+    ttFont["STAT"] = ttLib.newTable("STAT")
+    statTable = ttFont["STAT"].table = ot.STAT()
+    nameTable = ttFont["name"]
+    statTable.ElidedFallbackNameID = _addName(nameTable, elidedFallbackName)
+
+    # 'locations' contains data for AxisValue Format 4
+    axisRecords, axisValues = _buildAxisRecords(axes, nameTable)
+    if not locations:
+        statTable.Version = 0x00010001
+    else:
+        # We'll be adding Format 4 AxisValue records, which
+        # requires a higher table version
+        statTable.Version = 0x00010002
+        multiAxisValues = _buildAxisValuesFormat4(locations, axes, nameTable)
+        axisValues = multiAxisValues + axisValues
+
+    # Store AxisRecords
+    axisRecordArray = ot.AxisRecordArray()
+    axisRecordArray.Axis = axisRecords
+    # XXX these should not be hard-coded but computed automatically
+    statTable.DesignAxisRecordSize = 8
+    statTable.DesignAxisRecord = axisRecordArray
+    statTable.DesignAxisCount = len(axisRecords)
+
+    if axisValues:
+        # Store AxisValueRecords
+        axisValueArray = ot.AxisValueArray()
+        axisValueArray.AxisValue = axisValues
+        statTable.AxisValueArray = axisValueArray
+        statTable.AxisValueCount = len(axisValues)
+
+
+def _buildAxisRecords(axes, nameTable):
+    axisRecords = []
+    axisValues = []
+    for axisRecordIndex, axisDict in enumerate(axes):
+        axis = ot.AxisRecord()
+        axis.AxisTag = axisDict["tag"]
+        axis.AxisNameID = _addName(nameTable, axisDict["name"])
+        axis.AxisOrdering = axisDict.get("ordering", axisRecordIndex)
+        axisRecords.append(axis)
+
+        for axisVal in axisDict.get("values", ()):
+            axisValRec = ot.AxisValue()
+            axisValRec.AxisIndex = axisRecordIndex
+            axisValRec.Flags = axisVal.get("flags", 0)
+            axisValRec.ValueNameID = _addName(nameTable, axisVal['name'])
+
+            if "value" in axisVal:
+                axisValRec.Value = axisVal["value"]
+                if "linkedValue" in axisVal:
+                    axisValRec.Format = 3
+                    axisValRec.LinkedValue = axisVal["linkedValue"]
+                else:
+                    axisValRec.Format = 1
+            elif "nominalValue" in axisVal:
+                axisValRec.Format = 2
+                axisValRec.NominalValue = axisVal["nominalValue"]
+                axisValRec.RangeMinValue = axisVal.get("rangeMinValue", AXIS_VALUE_NEGATIVE_INFINITY)
+                axisValRec.RangeMaxValue = axisVal.get("rangeMaxValue", AXIS_VALUE_POSITIVE_INFINITY)
+            else:
+                raise ValueError("Can't determine format for AxisValue")
+
+            axisValues.append(axisValRec)
+    return axisRecords, axisValues
+
+
+def _buildAxisValuesFormat4(locations, axes, nameTable):
+    axisTagToIndex = {}
+    for axisRecordIndex, axisDict in enumerate(axes):
+        axisTagToIndex[axisDict["tag"]] = axisRecordIndex
+
+    axisValues = []
+    for axisLocationDict in locations:
+        axisValRec = ot.AxisValue()
+        axisValRec.Format = 4
+        axisValRec.ValueNameID = _addName(nameTable, axisLocationDict['name'])
+        axisValRec.Flags = axisLocationDict.get("flags", 0)
+        axisValueRecords = []
+        for tag, value in axisLocationDict["location"].items():
+            avr = ot.AxisValueRecord()
+            avr.AxisIndex = axisTagToIndex[tag]
+            avr.Value = value
+            axisValueRecords.append(avr)
+        axisValueRecords.sort(key=lambda avr: avr.AxisIndex)
+        axisValRec.AxisCount = len(axisValueRecords)
+        axisValRec.AxisValueRecord = axisValueRecords
+        axisValues.append(axisValRec)
+    return axisValues
+
+
+def _addName(nameTable, value):
+    if isinstance(value, int):
+        # Already a nameID
+        return value
+    if isinstance(value, str):
+        names = dict(en=value)
+    elif isinstance(value, dict):
+        names = value
+    else:
+        raise TypeError("value must be int, str or dict")
+    return nameTable.addMultilingualName(names)
diff --git a/Lib/fontTools/varLib/__init__.py b/Lib/fontTools/varLib/__init__.py
index 862decacd..f8ae30e29 100644
--- a/Lib/fontTools/varLib/__init__.py
+++ b/Lib/fontTools/varLib/__init__.py
@@ -202,30 +202,10 @@ def _add_stat(font, axes):
 	if "STAT" in font:
 		return
 
+	from ..otlLib.builder import buildStatTable
 	fvarTable = font['fvar']
-
-	STAT = font["STAT"] = newTable('STAT')
-	stat = STAT.table = ot.STAT()
-	stat.Version = 0x00010001
-
-	axisRecords = []
-	for i, a in enumerate(fvarTable.axes):
-		axis = ot.AxisRecord()
-		axis.AxisTag = Tag(a.axisTag)
-		axis.AxisNameID = a.axisNameID
-		axis.AxisOrdering = i
-		axisRecords.append(axis)
-
-	axisRecordArray = ot.AxisRecordArray()
-	axisRecordArray.Axis = axisRecords
-	# XXX these should not be hard-coded but computed automatically
-	stat.DesignAxisRecordSize = 8
-	stat.DesignAxisCount = len(axisRecords)
-	stat.DesignAxisRecord = axisRecordArray
-
-	# for the elided fallback name, we default to the base style name.
-	# TODO make this user-configurable via designspace document
-	stat.ElidedFallbackNameID = 2
+	axes = [dict(tag=a.axisTag, name=a.axisNameID) for a in fvarTable.axes]
+	buildStatTable(font, axes)
 
 
 def _add_gvar(font, masterModel, master_ttfs, tolerance=0.5, optimize=True):
diff --git a/Tests/fontBuilder/data/test_var.ttf.ttx b/Tests/fontBuilder/data/test_var.ttf.ttx
index bc1aae250..ed8fd3075 100644
--- a/Tests/fontBuilder/data/test_var.ttf.ttx
+++ b/Tests/fontBuilder/data/test_var.ttf.ttx
@@ -204,6 +204,9 @@
     <namerecord nameID="261" platformID="1" platEncID="0" langID="0x0" unicode="True">
       Right Up
     </namerecord>
+    <namerecord nameID="262" platformID="1" platEncID="0" langID="0x0" unicode="True">
+      Neutral
+    </namerecord>
     <namerecord nameID="1" platformID="1" platEncID="0" langID="0x4" unicode="True">
       HalloTestFont
     </namerecord>
@@ -237,6 +240,9 @@
     <namerecord nameID="261" platformID="3" platEncID="1" langID="0x409">
       Right Up
     </namerecord>
+    <namerecord nameID="262" platformID="3" platEncID="1" langID="0x409">
+      Neutral
+    </namerecord>
     <namerecord nameID="1" platformID="3" platEncID="1" langID="0x413">
       HalloTestFont
     </namerecord>
@@ -363,6 +369,86 @@
     </FeatureVariations>
   </GSUB>
 
+  <STAT>
+    <Version value="0x00010001"/>
+    <DesignAxisRecordSize value="8"/>
+    <!-- DesignAxisCount=4 -->
+    <DesignAxisRecord>
+      <Axis index="0">
+        <AxisTag value="LEFT"/>
+        <AxisNameID value="256"/>  <!-- Left -->
+        <AxisOrdering value="0"/>
+      </Axis>
+      <Axis index="1">
+        <AxisTag value="RGHT"/>
+        <AxisNameID value="257"/>  <!-- Right -->
+        <AxisOrdering value="1"/>
+      </Axis>
+      <Axis index="2">
+        <AxisTag value="UPPP"/>
+        <AxisNameID value="258"/>  <!-- Up -->
+        <AxisOrdering value="2"/>
+      </Axis>
+      <Axis index="3">
+        <AxisTag value="DOWN"/>
+        <AxisNameID value="259"/>  <!-- Down -->
+        <AxisOrdering value="3"/>
+      </Axis>
+    </DesignAxisRecord>
+    <!-- AxisValueCount=8 -->
+    <AxisValueArray>
+      <AxisValue index="0" Format="1">
+        <AxisIndex value="0"/>
+        <Flags value="2"/>
+        <ValueNameID value="262"/>  <!-- Neutral -->
+        <Value value="0.0"/>
+      </AxisValue>
+      <AxisValue index="1" Format="1">
+        <AxisIndex value="0"/>
+        <Flags value="0"/>
+        <ValueNameID value="256"/>  <!-- Left -->
+        <Value value="100.0"/>
+      </AxisValue>
+      <AxisValue index="2" Format="1">
+        <AxisIndex value="1"/>
+        <Flags value="2"/>
+        <ValueNameID value="262"/>  <!-- Neutral -->
+        <Value value="0.0"/>
+      </AxisValue>
+      <AxisValue index="3" Format="1">
+        <AxisIndex value="1"/>
+        <Flags value="0"/>
+        <ValueNameID value="257"/>  <!-- Right -->
+        <Value value="100.0"/>
+      </AxisValue>
+      <AxisValue index="4" Format="1">
+        <AxisIndex value="2"/>
+        <Flags value="2"/>
+        <ValueNameID value="262"/>  <!-- Neutral -->
+        <Value value="0.0"/>
+      </AxisValue>
+      <AxisValue index="5" Format="1">
+        <AxisIndex value="2"/>
+        <Flags value="0"/>
+        <ValueNameID value="258"/>  <!-- Up -->
+        <Value value="100.0"/>
+      </AxisValue>
+      <AxisValue index="6" Format="1">
+        <AxisIndex value="3"/>
+        <Flags value="2"/>
+        <ValueNameID value="262"/>  <!-- Neutral -->
+        <Value value="0.0"/>
+      </AxisValue>
+      <AxisValue index="7" Format="1">
+        <AxisIndex value="3"/>
+        <Flags value="0"/>
+        <ValueNameID value="259"/>  <!-- Down -->
+        <Value value="100.0"/>
+      </AxisValue>
+    </AxisValueArray>
+    <ElidedFallbackNameID value="2"/>  <!-- TotallyNormal -->
+  </STAT>
+
   <fvar>
 
     <!-- Left -->
diff --git a/Tests/fontBuilder/fontBuilder_test.py b/Tests/fontBuilder/fontBuilder_test.py
index bc7837c30..6368cb876 100644
--- a/Tests/fontBuilder/fontBuilder_test.py
+++ b/Tests/fontBuilder/fontBuilder_test.py
@@ -226,6 +226,13 @@ def test_build_var(tmpdir):
         featureTag="rclt",
     )
 
+    statAxes = []
+    for tag, minVal, defaultVal, maxVal, name in axes:
+        values = [dict(name="Neutral", value=defaultVal, flags=0x2),
+                  dict(name=name, value=maxVal)]
+        statAxes.append(dict(tag=tag, name=name, values=values))
+    fb.setupStat(statAxes)
+
     fb.setupOS2()
     fb.setupPost()
     fb.setupDummyDSIG()
diff --git a/Tests/otlLib/builder_test.py b/Tests/otlLib/builder_test.py
index 3675395fe..727d685f3 100644
--- a/Tests/otlLib/builder_test.py
+++ b/Tests/otlLib/builder_test.py
@@ -1,5 +1,9 @@
+import io
+import struct
+from fontTools.misc.fixedTools import floatToFixed
 from fontTools.misc.testTools import getXML
 from fontTools.otlLib import builder
+from fontTools import ttLib
 from fontTools.ttLib.tables import otTables
 import pytest
 
@@ -1106,6 +1110,291 @@ class ClassDefBuilderTest(object):
         assert not b.canAdd({"f"})
 
 
+buildStatTable_test_data = [
+    ([
+        dict(
+            tag="wght",
+            name="Weight",
+            values=[
+                dict(value=100, name='Thin'),
+                dict(value=400, name='Regular', flags=0x2),
+                dict(value=900, name='Black')])], None, "Regular", [
+        '  <STAT>',
+        '    <Version value="0x00010001"/>',
+        '    <DesignAxisRecordSize value="8"/>',
+        '    <!-- DesignAxisCount=1 -->',
+        '    <DesignAxisRecord>',
+        '      <Axis index="0">',
+        '        <AxisTag value="wght"/>',
+        '        <AxisNameID value="257"/>  <!-- Weight -->',
+        '        <AxisOrdering value="0"/>',
+        '      </Axis>',
+        '    </DesignAxisRecord>',
+        '    <!-- AxisValueCount=3 -->',
+        '    <AxisValueArray>',
+        '      <AxisValue index="0" Format="1">',
+        '        <AxisIndex value="0"/>',
+        '        <Flags value="0"/>',
+        '        <ValueNameID value="258"/>  <!-- Thin -->',
+        '        <Value value="100.0"/>',
+        '      </AxisValue>',
+        '      <AxisValue index="1" Format="1">',
+        '        <AxisIndex value="0"/>',
+        '        <Flags value="2"/>',
+        '        <ValueNameID value="256"/>  <!-- Regular -->',
+        '        <Value value="400.0"/>',
+        '      </AxisValue>',
+        '      <AxisValue index="2" Format="1">',
+        '        <AxisIndex value="0"/>',
+        '        <Flags value="0"/>',
+        '        <ValueNameID value="259"/>  <!-- Black -->',
+        '        <Value value="900.0"/>',
+        '      </AxisValue>',
+        '    </AxisValueArray>',
+        '    <ElidedFallbackNameID value="256"/>  <!-- Regular -->',
+        '  </STAT>']),
+    ([
+        dict(
+            tag="wght",
+            name=dict(en="Weight", nl="Gewicht"),
+            values=[
+                dict(value=100, name=dict(en='Thin', nl='Dun')),
+                dict(value=400, name='Regular', flags=0x2),
+                dict(value=900, name='Black'),
+            ]),
+        dict(
+            tag="wdth",
+            name="Width",
+            values=[
+                dict(value=50, name='Condensed'),
+                dict(value=100, name='Regular', flags=0x2),
+                dict(value=200, name='Extended')])], None, 2, [
+        '  <STAT>',
+        '    <Version value="0x00010001"/>',
+        '    <DesignAxisRecordSize value="8"/>',
+        '    <!-- DesignAxisCount=2 -->',
+        '    <DesignAxisRecord>',
+        '      <Axis index="0">',
+        '        <AxisTag value="wght"/>',
+        '        <AxisNameID value="256"/>  <!-- Weight -->',
+        '        <AxisOrdering value="0"/>',
+        '      </Axis>',
+        '      <Axis index="1">',
+        '        <AxisTag value="wdth"/>',
+        '        <AxisNameID value="260"/>  <!-- Width -->',
+        '        <AxisOrdering value="1"/>',
+        '      </Axis>',
+        '    </DesignAxisRecord>',
+        '    <!-- AxisValueCount=6 -->',
+        '    <AxisValueArray>',
+        '      <AxisValue index="0" Format="1">',
+        '        <AxisIndex value="0"/>',
+        '        <Flags value="0"/>',
+        '        <ValueNameID value="257"/>  <!-- Thin -->',
+        '        <Value value="100.0"/>',
+        '      </AxisValue>',
+        '      <AxisValue index="1" Format="1">',
+        '        <AxisIndex value="0"/>',
+        '        <Flags value="2"/>',
+        '        <ValueNameID value="258"/>  <!-- Regular -->',
+        '        <Value value="400.0"/>',
+        '      </AxisValue>',
+        '      <AxisValue index="2" Format="1">',
+        '        <AxisIndex value="0"/>',
+        '        <Flags value="0"/>',
+        '        <ValueNameID value="259"/>  <!-- Black -->',
+        '        <Value value="900.0"/>',
+        '      </AxisValue>',
+        '      <AxisValue index="3" Format="1">',
+        '        <AxisIndex value="1"/>',
+        '        <Flags value="0"/>',
+        '        <ValueNameID value="261"/>  <!-- Condensed -->',
+        '        <Value value="50.0"/>',
+        '      </AxisValue>',
+        '      <AxisValue index="4" Format="1">',
+        '        <AxisIndex value="1"/>',
+        '        <Flags value="2"/>',
+        '        <ValueNameID value="258"/>  <!-- Regular -->',
+        '        <Value value="100.0"/>',
+        '      </AxisValue>',
+        '      <AxisValue index="5" Format="1">',
+        '        <AxisIndex value="1"/>',
+        '        <Flags value="0"/>',
+        '        <ValueNameID value="262"/>  <!-- Extended -->',
+        '        <Value value="200.0"/>',
+        '      </AxisValue>',
+        '    </AxisValueArray>',
+        '    <ElidedFallbackNameID value="2"/>  <!-- missing from name table -->',
+        '  </STAT>']),
+    ([
+        dict(
+            tag="wght",
+            name="Weight",
+            values=[
+                dict(value=400, name='Regular', flags=0x2),
+                dict(value=600, linkedValue=650, name='Bold')])], None, 18, [
+        '  <STAT>',
+        '    <Version value="0x00010001"/>',
+        '    <DesignAxisRecordSize value="8"/>',
+        '    <!-- DesignAxisCount=1 -->',
+        '    <DesignAxisRecord>',
+        '      <Axis index="0">',
+        '        <AxisTag value="wght"/>',
+        '        <AxisNameID value="256"/>  <!-- Weight -->',
+        '        <AxisOrdering value="0"/>',
+        '      </Axis>',
+        '    </DesignAxisRecord>',
+        '    <!-- AxisValueCount=2 -->',
+        '    <AxisValueArray>',
+        '      <AxisValue index="0" Format="1">',
+        '        <AxisIndex value="0"/>',
+        '        <Flags value="2"/>',
+        '        <ValueNameID value="257"/>  <!-- Regular -->',
+        '        <Value value="400.0"/>',
+        '      </AxisValue>',
+        '      <AxisValue index="1" Format="3">',
+        '        <AxisIndex value="0"/>',
+        '        <Flags value="0"/>',
+        '        <ValueNameID value="258"/>  <!-- Bold -->',
+        '        <Value value="600.0"/>',
+        '        <LinkedValue value="650.0"/>',
+        '      </AxisValue>',
+        '    </AxisValueArray>',
+        '    <ElidedFallbackNameID value="18"/>  <!-- missing from name table -->',
+        '  </STAT>']),
+    ([
+        dict(
+            tag="opsz",
+            name="Optical Size",
+            values=[
+                dict(nominalValue=6, rangeMaxValue=10, name='Small'),
+                dict(rangeMinValue=10, nominalValue=14, rangeMaxValue=24, name='Text', flags=0x2),
+                dict(rangeMinValue=24, nominalValue=600, name='Display')])], None, 2, [
+        '  <STAT>',
+        '    <Version value="0x00010001"/>',
+        '    <DesignAxisRecordSize value="8"/>',
+        '    <!-- DesignAxisCount=1 -->',
+        '    <DesignAxisRecord>',
+        '      <Axis index="0">',
+        '        <AxisTag value="opsz"/>',
+        '        <AxisNameID value="256"/>  <!-- Optical Size -->',
+        '        <AxisOrdering value="0"/>',
+        '      </Axis>',
+        '    </DesignAxisRecord>',
+        '    <!-- AxisValueCount=3 -->',
+        '    <AxisValueArray>',
+        '      <AxisValue index="0" Format="2">',
+        '        <AxisIndex value="0"/>',
+        '        <Flags value="0"/>',
+        '        <ValueNameID value="257"/>  <!-- Small -->',
+        '        <NominalValue value="6.0"/>',
+        '        <RangeMinValue value="-32768.0"/>',
+        '        <RangeMaxValue value="10.0"/>',
+        '      </AxisValue>',
+        '      <AxisValue index="1" Format="2">',
+        '        <AxisIndex value="0"/>',
+        '        <Flags value="2"/>',
+        '        <ValueNameID value="258"/>  <!-- Text -->',
+        '        <NominalValue value="14.0"/>',
+        '        <RangeMinValue value="10.0"/>',
+        '        <RangeMaxValue value="24.0"/>',
+        '      </AxisValue>',
+        '      <AxisValue index="2" Format="2">',
+        '        <AxisIndex value="0"/>',
+        '        <Flags value="0"/>',
+        '        <ValueNameID value="259"/>  <!-- Display -->',
+        '        <NominalValue value="600.0"/>',
+        '        <RangeMinValue value="24.0"/>',
+        '        <RangeMaxValue value="32767.99998"/>',
+        '      </AxisValue>',
+        '    </AxisValueArray>',
+        '    <ElidedFallbackNameID value="2"/>  <!-- missing from name table -->',
+        '  </STAT>']),
+    ([
+        dict(
+            tag="wght",
+            name="Weight",
+            ordering=1,
+            values=[]),
+        dict(
+            tag="ABCD",
+            name="ABCDTest",
+            ordering=0,
+            values=[
+                dict(value=100, name="Regular", flags=0x2)])],
+     [dict(location=dict(wght=300, ABCD=100), name='Regular ABCD')], 18, [
+        '  <STAT>',
+        '    <Version value="0x00010002"/>',
+        '    <DesignAxisRecordSize value="8"/>',
+        '    <!-- DesignAxisCount=2 -->',
+        '    <DesignAxisRecord>',
+        '      <Axis index="0">',
+        '        <AxisTag value="wght"/>',
+        '        <AxisNameID value="256"/>  <!-- Weight -->',
+        '        <AxisOrdering value="1"/>',
+        '      </Axis>',
+        '      <Axis index="1">',
+        '        <AxisTag value="ABCD"/>',
+        '        <AxisNameID value="257"/>  <!-- ABCDTest -->',
+        '        <AxisOrdering value="0"/>',
+        '      </Axis>',
+        '    </DesignAxisRecord>',
+        '    <!-- AxisValueCount=2 -->',
+        '    <AxisValueArray>',
+        '      <AxisValue index="0" Format="4">',
+        '        <!-- AxisCount=2 -->',
+        '        <Flags value="0"/>',
+        '        <ValueNameID value="259"/>  <!-- Regular ABCD -->',
+        '        <AxisValueRecord index="0">',
+        '          <AxisIndex value="0"/>',
+        '          <Value value="300.0"/>',
+        '        </AxisValueRecord>',
+        '        <AxisValueRecord index="1">',
+        '          <AxisIndex value="1"/>',
+        '          <Value value="100.0"/>',
+        '        </AxisValueRecord>',
+        '      </AxisValue>',
+        '      <AxisValue index="1" Format="1">',
+        '        <AxisIndex value="1"/>',
+        '        <Flags value="2"/>',
+        '        <ValueNameID value="258"/>  <!-- Regular -->',
+        '        <Value value="100.0"/>',
+        '      </AxisValue>',
+        '    </AxisValueArray>',
+        '    <ElidedFallbackNameID value="18"/>  <!-- missing from name table -->',
+        '  </STAT>']),
+]
+
+
+@pytest.mark.parametrize("axes, axisValues, elidedFallbackName, expected_ttx", buildStatTable_test_data)
+def test_buildStatTable(axes, axisValues, elidedFallbackName, expected_ttx):
+    font = ttLib.TTFont()
+    font["name"] = ttLib.newTable("name")
+    font["name"].names = []
+    builder.buildStatTable(font, axes, axisValues, elidedFallbackName)
+    f = io.StringIO()
+    font.saveXML(f, tables=["STAT"])
+    ttx = f.getvalue().splitlines()
+    ttx = ttx[3:-2]  # strip XML header and <ttFont> element
+    assert expected_ttx == ttx
+    # Compile and round-trip
+    f = io.BytesIO()
+    font.save(f)
+    font = ttLib.TTFont(f)
+    f = io.StringIO()
+    font.saveXML(f, tables=["STAT"])
+    ttx = f.getvalue().splitlines()
+    ttx = ttx[3:-2]  # strip XML header and <ttFont> element
+    assert expected_ttx == ttx
+
+
+def test_stat_infinities():
+    negInf = floatToFixed(builder.AXIS_VALUE_NEGATIVE_INFINITY, 16)
+    assert struct.pack(">l", negInf) == b"\x80\x00\x00\x00"
+    posInf = floatToFixed(builder.AXIS_VALUE_POSITIVE_INFINITY, 16)
+    assert struct.pack(">l", posInf) == b"\x7f\xff\xff\xff"
+
+
 if __name__ == "__main__":
     import sys