diff --git a/Lib/fontTools/varLib/mutator.py b/Lib/fontTools/varLib/mutator.py
index 79a6f3d1b..dd6dd5ee5 100644
--- a/Lib/fontTools/varLib/mutator.py
+++ b/Lib/fontTools/varLib/mutator.py
@@ -9,7 +9,7 @@ from fontTools.misc.fixedTools import floatToFixedToFloat, otRound, floatToFixed
 from fontTools.pens.boundsPen import BoundsPen
 from fontTools.ttLib import TTFont, newTable
 from fontTools.ttLib.tables import ttProgram
-from fontTools.ttLib.tables._g_l_y_f import GlyphCoordinates
+from fontTools.ttLib.tables._g_l_y_f import GlyphCoordinates, flagOverlapSimple, OVERLAP_COMPOUND
 from fontTools.varLib import _GetCoordinates, _SetCoordinates
 from fontTools.varLib.models import (
 	supportScalar,
@@ -145,7 +145,7 @@ def interpolate_cff2_metrics(varfont, topDict, glyphOrder, loc):
 			hmtx[gname] = tuple(entry)
 
 
-def instantiateVariableFont(varfont, location, inplace=False):
+def instantiateVariableFont(varfont, location, inplace=False, overlap=True):
 	""" Generate a static instance from a variable TTFont and a dictionary
 	defining the desired location along the variable font's axes.
 	The location values must be specified as user-space coordinates, e.g.:
@@ -154,6 +154,10 @@ def instantiateVariableFont(varfont, location, inplace=False):
 
 	By default, a new TTFont object is returned. If ``inplace`` is True, the
 	input varfont is modified and reduced to a static font.
+
+	When the overlap parameter is defined as True,
+	OVERLAP_SIMPLE and OVERLAP_COMPOUND bits are set to 1.  See
+	https://docs.microsoft.com/en-us/typography/opentype/spec/glyf
 	"""
 	if not inplace:
 		# make a copy to leave input varfont unmodified
@@ -308,6 +312,15 @@ def instantiateVariableFont(varfont, location, inplace=False):
 				addidef = any(op.startswith("GETVARIATION") for op in instructions)
 				if addidef:
 					break
+		if overlap:
+			for glyph_name in glyf.keys():
+				glyph = glyf[glyph_name]
+				# Set OVERLAP_COMPOUND bit for compound glyphs
+				if glyph.isComposite():
+					glyph.components[0].flags |= OVERLAP_COMPOUND
+				# Set OVERLAP_SIMPLE bit for simple glyphs
+				elif glyph.numberOfContours > 0:
+					glyph.flags[0] |= flagOverlapSimple
 	if addidef:
 		log.info("Adding IDEF to fpgm table for GETVARIATION opcode")
 		asm = []
diff --git a/Tests/varLib/data/test_results/Mutator.ttx b/Tests/varLib/data/test_results/Mutator.ttx
index a106d213b..fac0997a6 100644
--- a/Tests/varLib/data/test_results/Mutator.ttx
+++ b/Tests/varLib/data/test_results/Mutator.ttx
@@ -154,7 +154,7 @@
 
     <TTGlyph name=".notdef" xMin="80" yMin="0" xMax="560" yMax="666">
       <contour>
-        <pt x="83" y="0" on="1"/>
+        <pt x="83" y="0" on="1" overlap="1"/>
         <pt x="503" y="666" on="1"/>
         <pt x="557" y="666" on="1"/>
         <pt x="137" y="0" on="1"/>
@@ -190,7 +190,7 @@
 
     <TTGlyph name="uni0024" xMin="51" yMin="-115" xMax="474" yMax="746">
       <contour>
-        <pt x="251" y="31" on="1"/>
+        <pt x="251" y="31" on="1" overlap="1"/>
         <pt x="309" y="31" on="0"/>
         <pt x="379" y="92" on="0"/>
         <pt x="379" y="144" on="1"/>
@@ -262,7 +262,7 @@
 
     <TTGlyph name="uni0024.nostroke" xMin="51" yMin="-115" xMax="474" yMax="746">
       <contour>
-        <pt x="251" y="31" on="1"/>
+        <pt x="251" y="31" on="1" overlap="1"/>
         <pt x="308" y="31" on="0"/>
         <pt x="377" y="90" on="0"/>
         <pt x="377" y="142" on="1"/>
@@ -334,7 +334,7 @@
 
     <TTGlyph name="uni0041" xMin="7" yMin="0" xMax="656" yMax="670">
       <contour>
-        <pt x="7" y="0" on="1"/>
+        <pt x="7" y="0" on="1" overlap="1"/>
         <pt x="7" y="38" on="1"/>
         <pt x="104" y="53" on="1"/>
         <pt x="124" y="53" on="1"/>
@@ -370,7 +370,7 @@
 
     <TTGlyph name="uni0061" xMin="42" yMin="-14" xMax="511" yMax="490">
       <contour>
-        <pt x="42" y="110" on="1"/>
+        <pt x="42" y="110" on="1" overlap="1"/>
         <pt x="42" y="157" on="0"/>
         <pt x="110" y="229" on="0"/>
         <pt x="214" y="265" on="1"/>
diff --git a/Tests/varLib/data/test_results/Mutator_Getvar-instance.ttx b/Tests/varLib/data/test_results/Mutator_Getvar-instance.ttx
index a20f0e4fa..28e0766a7 100755
--- a/Tests/varLib/data/test_results/Mutator_Getvar-instance.ttx
+++ b/Tests/varLib/data/test_results/Mutator_Getvar-instance.ttx
@@ -168,7 +168,7 @@
 
     <TTGlyph name="a" xMin="38" yMin="-12" xMax="388" yMax="468">
       <contour>
-        <pt x="312" y="0" on="1"/>
+        <pt x="312" y="0" on="1" overlap="1"/>
         <pt x="312" y="64" on="1"/>
         <pt x="244" y="-12" on="1"/>
         <pt x="180" y="-12" on="1"/>
@@ -200,7 +200,7 @@
 
     <TTGlyph name="b" xMin="76" yMin="-12" xMax="426" yMax="628">
       <contour>
-        <pt x="218" y="468" on="1"/>
+        <pt x="218" y="468" on="1" overlap="1"/>
         <pt x="284" y="468" on="1"/>
         <pt x="426" y="316" on="1"/>
         <pt x="426" y="140" on="1"/>
@@ -229,7 +229,7 @@
     <TTGlyph name="nonmarkingreturn"/><!-- contains no outline data -->
 
     <TTGlyph name="q" xMin="38" yMin="-172" xMax="388" yMax="468">
-      <component glyphName="b" x="464" y="456" scale="-0.99994" flags="0x4"/>
+      <component glyphName="b" x="464" y="456" scale="-0.99994" flags="0x404"/>
     </TTGlyph>
 
     <TTGlyph name="space"/><!-- contains no outline data -->
diff --git a/Tests/varLib/data/test_results/Mutator_IUP-instance.ttx b/Tests/varLib/data/test_results/Mutator_IUP-instance.ttx
index 1800479b1..1f7b651f0 100755
--- a/Tests/varLib/data/test_results/Mutator_IUP-instance.ttx
+++ b/Tests/varLib/data/test_results/Mutator_IUP-instance.ttx
@@ -157,7 +157,7 @@
 
     <TTGlyph name="a" xMin="38" yMin="-12" xMax="388" yMax="468">
       <contour>
-        <pt x="312" y="0" on="1"/>
+        <pt x="312" y="0" on="1" overlap="1"/>
         <pt x="312" y="64" on="1"/>
         <pt x="244" y="-12" on="1"/>
         <pt x="180" y="-12" on="1"/>
@@ -185,7 +185,7 @@
 
     <TTGlyph name="b" xMin="76" yMin="-12" xMax="426" yMax="628">
       <contour>
-        <pt x="218" y="468" on="1"/>
+        <pt x="218" y="468" on="1" overlap="1"/>
         <pt x="284" y="468" on="1"/>
         <pt x="426" y="316" on="1"/>
         <pt x="426" y="140" on="1"/>
@@ -214,7 +214,7 @@
     <TTGlyph name="nonmarkingreturn"/><!-- contains no outline data -->
 
     <TTGlyph name="q" xMin="38" yMin="-172" xMax="388" yMax="468">
-      <component glyphName="b" x="464" y="456" scale="-0.99994" flags="0x4"/>
+      <component glyphName="b" x="464" y="456" scale="-0.99994" flags="0x404"/>
     </TTGlyph>
 
     <TTGlyph name="space"/><!-- contains no outline data -->