diff --git a/font/sfnt/cmap.go b/font/sfnt/cmap.go
index 19b0a9d..be302d2 100644
--- a/font/sfnt/cmap.go
+++ b/font/sfnt/cmap.go
@@ -19,6 +19,9 @@
 
 	psidUnicode2BMPOnly        = 3
 	psidUnicode2FullRepertoire = 4
+	// Note that FontForge may generate a bogus Platform Specific ID (value 10)
+	// for the Unicode Platform ID (value 0). See
+	// https://github.com/fontforge/fontforge/issues/2728
 
 	psidMacintoshRoman = 0
 
diff --git a/font/sfnt/sfnt_test.go b/font/sfnt/sfnt_test.go
index 4b72221..f1c6ac1 100644
--- a/font/sfnt/sfnt_test.go
+++ b/font/sfnt/sfnt_test.go
@@ -89,7 +89,7 @@
 }
 
 func TestGlyphIndex(t *testing.T) {
-	data, err := ioutil.ReadFile(filepath.FromSlash("../testdata/CFFTest.otf"))
+	data, err := ioutil.ReadFile(filepath.FromSlash("../testdata/cmapTest.ttf"))
 	if err != nil {
 		t.Fatal(err)
 	}
@@ -120,27 +120,64 @@
 		r    rune
 		want GlyphIndex
 	}{
-		{'0', 1},
-		{'1', 2},
-		{'Q', 3},
-		// TODO: add the U+00E0 non-ASCII Latin-1 Supplement rune to
-		// CFFTest.otf and change 0 to something non-zero.
-		{'\u00e0', 0},
-		{'\u4e2d', 4},
-		// TODO: add a rune >= U+00010000 to CFFTest.otf?
-
-		// Glyphs that aren't present in CFFTest.otf.
+		// Glyphs that aren't present in cmapTest.ttf.
 		{'?', 0},
 		{'\ufffd', 0},
 		{'\U0001f4a9', 0},
+
+		// For a .TTF file, FontForge maps:
+		//	- ".notdef"          to glyph index 0.
+		//	- ".null"            to glyph index 1.
+		//	- "nonmarkingreturn" to glyph index 2.
+
+		{'/', 0},
+		{'0', 3},
+		{'1', 4},
+		{'2', 5},
+		{'3', 0},
+
+		{'@', 0},
+		{'A', 6},
+		{'B', 7},
+		{'C', 0},
+
+		{'`', 0},
+		{'a', 8},
+		{'b', 0},
+
+		// Of the remaining runes, only U+00FF LATIN SMALL LETTER Y WITH
+		// DIAERESIS is in both the Mac Roman encoding and the cmapTest.ttf
+		// font file.
+		{'\u00fe', 0},
+		{'\u00ff', 9},
+		{'\u0100', 10},
+		{'\u0101', 11},
+		{'\u0102', 0},
+
+		{'\u4e2c', 0},
+		{'\u4e2d', 12},
+		{'\u4e2e', 0},
+
+		/*
+			TODO: support runes above U+FFFF, i.e. cmap format 12.
+
+			{'\U0001f0a0', 0},
+			{'\U0001f0a1', 13},
+			{'\U0001f0a2', 0},
+
+			{'\U0001f0b0', 0},
+			{'\U0001f0b1', 14},
+			{'\U0001f0b2', 15},
+			{'\U0001f0b3', 0},
+		*/
 	}
 
 	var b Buffer
 	for _, tc := range testCases {
 		want := tc.want
-		// cmap format 0, with the Macintosh Roman encoding, can't represent
-		// U+4E2D.
-		if cmapFormat == 0 && tc.r == '\u4e2d' {
+		// cmap format 0, with the Macintosh Roman encoding, can only represent
+		// a limited set of non-ASCII runes, e.g. U+00FF.
+		if cmapFormat == 0 && tc.r > '\u007f' && tc.r != '\u00ff' {
 			want = 0
 		}
 
diff --git a/font/testdata/cmapTest.sfd b/font/testdata/cmapTest.sfd
new file mode 100644
index 0000000..34c7cd6
--- /dev/null
+++ b/font/testdata/cmapTest.sfd
@@ -0,0 +1,265 @@
+SplineFontDB: 3.0
+FontName: cmapTest
+FullName: cmapTest
+FamilyName: cmapTest
+Weight: Regular
+Copyright: Copyright 2016 The Go Authors. All rights reserved.\nUse of this font is governed by a BSD-style license that can be found at https://golang.org/LICENSE.
+Version: 001.000
+ItalicAngle: -11.25
+UnderlinePosition: -204
+UnderlineWidth: 102
+Ascent: 1638
+Descent: 410
+LayerCount: 2
+Layer: 0 1 "Back"  1
+Layer: 1 1 "Fore"  0
+XUID: [1021 367 888937226 7862908]
+FSType: 8
+OS2Version: 0
+OS2_WeightWidthSlopeOnly: 0
+OS2_UseTypoMetrics: 1
+CreationTime: 1484386143
+ModificationTime: 1486021330
+PfmFamily: 17
+TTFWeight: 400
+TTFWidth: 5
+LineGap: 184
+VLineGap: 0
+OS2TypoAscent: 0
+OS2TypoAOffset: 1
+OS2TypoDescent: 0
+OS2TypoDOffset: 1
+OS2TypoLinegap: 184
+OS2WinAscent: 0
+OS2WinAOffset: 1
+OS2WinDescent: 0
+OS2WinDOffset: 1
+HheadAscent: 0
+HheadAOffset: 1
+HheadDescent: 0
+HheadDOffset: 1
+OS2Vendor: 'PfEd'
+MarkAttachClasses: 1
+DEI: 91125
+LangName: 1033 
+Encoding: UnicodeFull
+UnicodeInterp: none
+NameList: Adobe Glyph List
+DisplaySize: -24
+AntiAlias: 1
+FitToEm: 1
+WinInfo: 126976 32 23
+BeginPrivate: 0
+EndPrivate
+TeXData: 1 0 0 346030 173015 115343 0 -1048576 115343 783286 444596 497025 792723 393216 433062 380633 303038 157286 324010 404750 52429 2506097 1059062 262144
+BeginChars: 1114112 13
+
+StartChar: zero
+Encoding: 48 48 0
+Width: 800
+VWidth: 0
+Flags: W
+LayerCount: 2
+Fore
+SplineSet
+0 0 m 29,0,-1
+ 400 800 l 25,1,-1
+ 800 0 l 25,2,-1
+ 0 0 l 29,0,-1
+EndSplineSet
+Validated: 1
+EndChar
+
+StartChar: one
+Encoding: 49 49 1
+Width: 800
+VWidth: 0
+Flags: W
+LayerCount: 2
+Fore
+SplineSet
+0 0 m 29,0,-1
+ 400 800 l 25,1,-1
+ 800 0 l 25,2,-1
+ 0 0 l 29,0,-1
+EndSplineSet
+Validated: 1
+EndChar
+
+StartChar: two
+Encoding: 50 50 2
+Width: 800
+VWidth: 0
+Flags: W
+LayerCount: 2
+Fore
+SplineSet
+0 0 m 29,0,-1
+ 400 800 l 25,1,-1
+ 800 0 l 25,2,-1
+ 0 0 l 29,0,-1
+EndSplineSet
+Validated: 1
+EndChar
+
+StartChar: A
+Encoding: 65 65 3
+Width: 800
+VWidth: 0
+Flags: W
+LayerCount: 2
+Fore
+SplineSet
+0 0 m 29,0,-1
+ 400 800 l 25,1,-1
+ 800 0 l 25,2,-1
+ 0 0 l 29,0,-1
+EndSplineSet
+Validated: 1
+EndChar
+
+StartChar: uni4E2D
+Encoding: 20013 20013 4
+Width: 800
+VWidth: 0
+Flags: W
+LayerCount: 2
+Fore
+SplineSet
+0 0 m 29,0,-1
+ 400 800 l 25,1,-1
+ 800 0 l 25,2,-1
+ 0 0 l 29,0,-1
+EndSplineSet
+Validated: 1
+EndChar
+
+StartChar: u1F0A1
+Encoding: 127137 127137 5
+Width: 800
+VWidth: 0
+Flags: W
+LayerCount: 2
+Fore
+SplineSet
+0 0 m 29,0,-1
+ 400 800 l 25,1,-1
+ 800 0 l 25,2,-1
+ 0 0 l 29,0,-1
+EndSplineSet
+Validated: 1
+EndChar
+
+StartChar: ydieresis
+Encoding: 255 255 6
+Width: 800
+VWidth: 0
+Flags: W
+LayerCount: 2
+Fore
+SplineSet
+0 0 m 29,0,-1
+ 400 800 l 25,1,-1
+ 800 0 l 25,2,-1
+ 0 0 l 29,0,-1
+EndSplineSet
+Validated: 1
+EndChar
+
+StartChar: Amacron
+Encoding: 256 256 7
+Width: 800
+VWidth: 0
+Flags: W
+LayerCount: 2
+Fore
+SplineSet
+0 0 m 29,0,-1
+ 400 800 l 25,1,-1
+ 800 0 l 25,2,-1
+ 0 0 l 29,0,-1
+EndSplineSet
+Validated: 1
+EndChar
+
+StartChar: amacron
+Encoding: 257 257 8
+Width: 800
+VWidth: 0
+Flags: W
+LayerCount: 2
+Fore
+SplineSet
+0 0 m 29,0,-1
+ 400 800 l 25,1,-1
+ 800 0 l 25,2,-1
+ 0 0 l 29,0,-1
+EndSplineSet
+Validated: 1
+EndChar
+
+StartChar: B
+Encoding: 66 66 9
+Width: 800
+VWidth: 0
+Flags: W
+LayerCount: 2
+Fore
+SplineSet
+0 0 m 29,0,-1
+ 400 800 l 25,1,-1
+ 800 0 l 25,2,-1
+ 0 0 l 29,0,-1
+EndSplineSet
+Validated: 1
+EndChar
+
+StartChar: a
+Encoding: 97 97 10
+Width: 800
+VWidth: 0
+Flags: W
+LayerCount: 2
+Fore
+SplineSet
+0 0 m 29,0,-1
+ 400 800 l 25,1,-1
+ 800 0 l 25,2,-1
+ 0 0 l 29,0,-1
+EndSplineSet
+Validated: 1
+EndChar
+
+StartChar: u1F0B1
+Encoding: 127153 127153 11
+Width: 800
+VWidth: 0
+Flags: W
+LayerCount: 2
+Fore
+SplineSet
+0 0 m 29,0,-1
+ 400 800 l 25,1,-1
+ 800 0 l 25,2,-1
+ 0 0 l 29,0,-1
+EndSplineSet
+Validated: 1
+EndChar
+
+StartChar: u1F0B2
+Encoding: 127154 127154 12
+Width: 800
+VWidth: 0
+Flags: W
+LayerCount: 2
+Fore
+SplineSet
+0 0 m 29,0,-1
+ 400 800 l 25,1,-1
+ 800 0 l 25,2,-1
+ 0 0 l 29,0,-1
+EndSplineSet
+Validated: 1
+EndChar
+EndChars
+EndSplineFont
diff --git a/font/testdata/cmapTest.ttf b/font/testdata/cmapTest.ttf
new file mode 100644
index 0000000..ebe6be2
--- /dev/null
+++ b/font/testdata/cmapTest.ttf
Binary files differ