diff --git a/tests/filters/decomposeTransformedComponents_test.py b/tests/filters/decomposeTransformedComponents_test.py
index d66a42d14..54a79c57b 100644
--- a/tests/filters/decomposeTransformedComponents_test.py
+++ b/tests/filters/decomposeTransformedComponents_test.py
@@ -93,3 +93,94 @@ def test_decompose_compatibly(self, FontClass):
         ).process()
         assert len(glyphsets[0]["base"]) == 1
         assert len(glyphsets[1]["base"]) == 1
+
+    def test_decompose_compatibly_nested_transformed_components(self, FontClass):
+        # This replicates three glyphs from the 'changa.zip' test fonts at
+        # https://github.com/googlefonts/ufo2ft/issues/621
+        # In both fonts, the "exclam" glyph is made of one simple contour and one
+        # component ("period"); "exclamdown" in turn is made of one "exclam" component
+        # that is flipped vertically and horizontally; "period" is a single contour.
+        # But only in the Bold.ufo, the "exclam" contains a scaled down "period"; in
+        # the Regular.ufo, the "period" component only has an offset.
+        # This would previously trigger a situation whereby after "exclamdown" was
+        # decomposed, its points were no longer interpolation compatible across masters
+        # because the order in which the contours were decomposed was different.
+        # This is because filters used to modify glyphs in-place in alphabetical order,
+        # so 'exclam' comes before 'exclamdown', and in the Bold.ufo, 'exclam' has
+        # a 2x3 transform so is decomposed (with the period appended at the end), but
+        # then 'exclamdown' needs decomposing as well (for it's flipped) and the
+        # already decomposed 'exclam' contours are drawn onto it in the same order;
+        # whereas in Regular.ufo, the 'exclam' does not contain transformed components
+        # so it's kept as composite (for the time being, it will be decomposed later on
+        # because it's mixed), but when it's the turn of 'exclamdown', the period's
+        # contour gets appended to it before the rest of the rest of the 'exclam'
+        # (deepCopyContours follows a post-order depth-first traversal so the children
+        # get decomposed before the parent) -- leading to cu2qu crashing... Pfew!
+        regular_ufo = FontClass()
+        period = regular_ufo.newGlyph("period")
+        period.width = 230
+        pen = period.getPen()
+        pen.moveTo((50, 62))
+        pen.curveTo((50, 13), (61, -6), (115, -6))
+        pen.curveTo((168, -6), (180, 13), (180, 62))
+        pen.curveTo((180, 110), (168, 131), (115, 131))
+        pen.curveTo((61, 131), (50, 110), (50, 62))
+        pen.closePath()
+
+        exclam = regular_ufo.newGlyph("exclam")
+        exclam.width = 250
+        pen = exclam.getPen()
+        pen.moveTo((93, 196))
+        pen.lineTo((156, 196))
+        pen.lineTo((186, 627))
+        pen.curveTo((186, 637), (181, 645), (161, 645))
+        pen.lineTo((87, 645))
+        pen.curveTo((67, 645), (63, 637), (63, 627))
+        pen.closePath()
+        pen.addComponent("period", (1, 0, 0, 1, 10, 0))
+
+        exclamdown = regular_ufo.newGlyph("exclamdown")
+        exclamdown.width = 250
+        pen = exclamdown.getPen()
+        pen.addComponent("exclam", (-1, 0, 0, -1, 250, 509))
+
+        bold_ufo = FontClass()
+        period = bold_ufo.newGlyph("period")
+        period.width = 277
+        pen = period.getPen()
+        pen.moveTo((30, 99))
+        pen.curveTo((30, 23), (50, -6), (139, -6))
+        pen.curveTo((227, -6), (247, 23), (247, 99))
+        pen.curveTo((247, 175), (227, 206), (139, 206))
+        pen.curveTo((50, 206), (30, 175), (30, 99))
+        pen.closePath()
+
+        exclam = bold_ufo.newGlyph("exclam")
+        exclam.width = 297
+        pen = exclam.getPen()
+        pen.moveTo((84, 230))
+        pen.lineTo((214, 230))
+        pen.lineTo((254, 618))
+        pen.curveTo((254, 633), (247, 645), (217, 645))
+        pen.lineTo((81, 645))
+        pen.curveTo((51, 645), (44, 633), (44, 618))
+        pen.closePath()
+        pen.addComponent("period", (0.87, 0, 0, 0.87, 28, -1))
+
+        exclamdown = bold_ufo.newGlyph("exclamdown")
+        exclamdown.width = 297
+        pen = exclamdown.getPen()
+        pen.addComponent("exclam", (-1, 0, 0, -1, 298, 509))
+
+        # We test that, even with DecomposeTransformedComponentsFilter(pre=True) and
+        # the above nested/transformed/mixed component setup, we don't crash cu2qu
+        # with errors about masters with inconsistent contour order after decomposition
+        # of "exclamdown".
+        glyphsets = TTFInterpolatablePreProcessor(
+            [regular_ufo, bold_ufo],
+            filters=[DecomposeTransformedComponentsFilter(pre=True)],
+        ).process()
+        assert len(glyphsets[0]["exclam"]) == 2
+        assert len(glyphsets[0]["exclamdown"]) == 2
+        assert len(glyphsets[1]["exclam"]) == 2
+        assert len(glyphsets[1]["exclamdown"]) == 2