diff --git a/font/sfnt/cmap.go b/font/sfnt/cmap.go
index 9db98a8..e6e114e 100644
--- a/font/sfnt/cmap.go
+++ b/font/sfnt/cmap.go
@@ -167,6 +167,8 @@
 			offset: u16(buf[6*len(entries)+2+2*i:]),
 		}
 	}
+	indexesBase := f.cmap.offset + offset
+	indexesLength := f.cmap.length - offset
 
 	f.cached.glyphIndex = func(f *Font, b *Buffer, r rune) (GlyphIndex, error) {
 		if uint32(r) > 0xffff {
@@ -184,11 +186,15 @@
 			} else if entry.offset == 0 {
 				return GlyphIndex(c + entry.delta), nil
 			} else {
-				// TODO: support the glyphIdArray as per
-				// https://www.microsoft.com/typography/OTSPEC/cmap.htm
-				//
-				// This will probably use the *Font and *Buffer arguments.
-				return 0, errUnsupportedCmapFormat
+				offset := uint32(entry.offset) + 2*uint32(h-len(entries)+int(c-entry.start))
+				if offset > indexesLength || offset+2 > indexesLength {
+					return 0, errInvalidCmapTable
+				}
+				x, err := b.view(&f.src, int(indexesBase+offset), 2)
+				if err != nil {
+					return 0, err
+				}
+				return GlyphIndex(u16(x)), nil
 			}
 		}
 		return 0, nil
diff --git a/font/sfnt/sfnt.go b/font/sfnt/sfnt.go
index 61281e7..b7f4bdc 100644
--- a/font/sfnt/sfnt.go
+++ b/font/sfnt/sfnt.go
@@ -73,7 +73,6 @@
 
 	errUnsupportedCFFVersion           = errors.New("sfnt: unsupported CFF version")
 	errUnsupportedCmapEncodings        = errors.New("sfnt: unsupported cmap encodings")
-	errUnsupportedCmapFormat           = errors.New("sfnt: unsupported cmap format")
 	errUnsupportedCompoundGlyph        = errors.New("sfnt: unsupported compound glyph")
 	errUnsupportedGlyphDataLength      = errors.New("sfnt: unsupported glyph data length")
 	errUnsupportedRealNumberEncoding   = errors.New("sfnt: unsupported real number encoding")
diff --git a/font/sfnt/sfnt_test.go b/font/sfnt/sfnt_test.go
index c68d78c..c6d6741 100644
--- a/font/sfnt/sfnt_test.go
+++ b/font/sfnt/sfnt_test.go
@@ -88,6 +88,62 @@
 	}
 }
 
+func TestGoRegularGlyphIndex(t *testing.T) {
+	f, err := Parse(goregular.TTF)
+	if err != nil {
+		t.Fatalf("Parse: %v", err)
+	}
+
+	testCases := []struct {
+		r    rune
+		want GlyphIndex
+	}{
+		// Glyphs that aren't present in Go Regular.
+		{'\u001f', 0}, // U+001F <control>
+		{'\u0200', 0}, // U+0200 LATIN CAPITAL LETTER A WITH DOUBLE GRAVE
+		{'\u2000', 0}, // U+2000 EN QUAD
+
+		// The want values below can be verified by running the ttx tool on
+		// Go-Regular.ttf.
+		//
+		// The actual values are ad hoc, and result from whatever tools the
+		// Bigelow & Holmes type foundry used and the order in which they
+		// crafted the glyphs. They may change over time as newer versions of
+		// the font are released. In practice, though, running this test with
+		// coverage analysis suggests that it covers both the zero and non-zero
+		// cmapEntry16.offset cases for a format-4 cmap table.
+
+		{'\u0020', 3},   // U+0020 SPACE
+		{'\u0021', 4},   // U+0021 EXCLAMATION MARK
+		{'\u0022', 5},   // U+0022 QUOTATION MARK
+		{'\u0023', 6},   // U+0023 NUMBER SIGN
+		{'\u0024', 223}, // U+0024 DOLLAR SIGN
+		{'\u0025', 7},   // U+0025 PERCENT SIGN
+		{'\u0026', 8},   // U+0026 AMPERSAND
+		{'\u0027', 9},   // U+0027 APOSTROPHE
+
+		{'\u03bd', 423}, // U+03BD GREEK SMALL LETTER NU
+		{'\u03be', 424}, // U+03BE GREEK SMALL LETTER XI
+		{'\u03bf', 438}, // U+03BF GREEK SMALL LETTER OMICRON
+		{'\u03c0', 208}, // U+03C0 GREEK SMALL LETTER PI
+		{'\u03c1', 425}, // U+03C1 GREEK SMALL LETTER RHO
+		{'\u03c2', 426}, // U+03C2 GREEK SMALL LETTER FINAL SIGMA
+	}
+
+	var b Buffer
+	for _, tc := range testCases {
+		got, err := f.GlyphIndex(&b, tc.r)
+		if err != nil {
+			t.Errorf("r=%q: %v", tc.r, err)
+			continue
+		}
+		if got != tc.want {
+			t.Errorf("r=%q: got %d, want %d", tc.r, got, tc.want)
+			continue
+		}
+	}
+}
+
 func TestGlyphIndex(t *testing.T) {
 	data, err := ioutil.ReadFile(filepath.FromSlash("../testdata/cmapTest.ttf"))
 	if err != nil {