diff --git a/Tests/ttLib/data/Test-Regular.ttf b/Tests/ttLib/data/Test-Regular.ttf
new file mode 100644
index 000000000..db03587bb
Binary files /dev/null and b/Tests/ttLib/data/Test-Regular.ttf differ
diff --git a/Tests/ttLib/reorderGlyphs_test.py b/Tests/ttLib/reorderGlyphs_test.py
new file mode 100644
index 000000000..cfda2d285
--- /dev/null
+++ b/Tests/ttLib/reorderGlyphs_test.py
@@ -0,0 +1,77 @@
+import pytest
+
+from pathlib import Path
+from fontTools.ttLib import TTFont
+from fontTools.ttLib.reorderGlyphs import reorderGlyphs
+
+DATA_DIR = Path(__file__).parent / "data"
+
+
+@pytest.mark.parametrize("lazy", [True, False, None])
+def test_reorder_glyphs(lazy):
+    font_path = DATA_DIR / "Test-Regular.ttf"
+    font = TTFont(str(font_path), lazy=lazy)
+    old_coverage1 = list(
+        font["GSUB"].table.LookupList.Lookup[0].SubTable[0].Coverage[0].glyphs
+    )
+    old_coverage2 = list(
+        font["GPOS"].table.LookupList.Lookup[0].SubTable[0].Coverage.glyphs
+    )
+
+    ga = font.getGlyphOrder()
+    ga = [ga[0]] + list(reversed(ga[1:]))
+    reorderGlyphs(font, ga)
+
+    new_coverage1 = list(
+        font["GSUB"].table.LookupList.Lookup[0].SubTable[0].Coverage[0].glyphs
+    )
+    new_coverage2 = list(
+        font["GPOS"].table.LookupList.Lookup[0].SubTable[0].Coverage.glyphs
+    )
+
+    assert list(reversed(old_coverage1)) == new_coverage1
+    assert list(reversed(old_coverage2)) == new_coverage2
+
+
+def test_ttfont_reorder_glyphs():
+    font_path = DATA_DIR / "Test-Regular.ttf"
+    font = TTFont(str(font_path))
+    ga = font.getGlyphOrder()
+    ga = [ga[0]] + list(reversed(ga[1:]))
+
+    old_coverage1 = list(
+        font["GSUB"].table.LookupList.Lookup[0].SubTable[0].Coverage[0].glyphs
+    )
+    old_coverage2 = list(
+        font["GPOS"].table.LookupList.Lookup[0].SubTable[0].Coverage.glyphs
+    )
+
+    font.reorderGlyphs(ga)
+
+    new_coverage1 = list(
+        font["GSUB"].table.LookupList.Lookup[0].SubTable[0].Coverage[0].glyphs
+    )
+    new_coverage2 = list(
+        font["GPOS"].table.LookupList.Lookup[0].SubTable[0].Coverage.glyphs
+    )
+
+    assert list(reversed(old_coverage1)) == new_coverage1
+    assert list(reversed(old_coverage2)) == new_coverage2
+
+
+def test_reorder_glyphs_bad_length(caplog):
+    font_path = DATA_DIR / "Test-Regular.ttf"
+    font = TTFont(str(font_path))
+    with pytest.raises(ValueError) as ex:
+        reorderGlyphs(font, ["A"])
+    assert "New glyph order contains 1 glyphs" in str(ex.value)
+
+
+def test_reorder_glyphs_bad_set(caplog):
+    font_path = DATA_DIR / "Test-Regular.ttf"
+    font = TTFont(str(font_path))
+    ga = list(font.getGlyphOrder()) + ["AA"]
+    ga.pop(1)
+    with pytest.raises(ValueError) as ex:
+        reorderGlyphs(font, ga)
+    assert "New glyph order does not contain the same set of glyphs" in str(ex.value)