diff --git a/Lib/ufo2ft/filters/transformations.py b/Lib/ufo2ft/filters/transformations.py
index a7fe88e37..ecf8fbaac 100644
--- a/Lib/ufo2ft/filters/transformations.py
+++ b/Lib/ufo2ft/filters/transformations.py
@@ -1,5 +1,3 @@
-from __future__ import print_function, division, absolute_import, unicode_literals
-
 import math
 from collections import namedtuple
 import logging
@@ -7,38 +5,30 @@
 from ufo2ft.fontInfoData import getAttrWithFallback
 from ufo2ft.filters import BaseFilter
 
-from fontTools.misc.py23 import round
 from fontTools.misc.fixedTools import otRound
 from fontTools.misc.transform import Transform, Identity
-from fontTools.pens.recordingPen import RecordingPen
-from fontTools.pens.transformPen import TransformPen as _TransformPen
+from fontTools.pens.recordingPen import RecordingPointPen
+from fontTools.pens.transformPen import TransformPointPen as _TransformPointPen
 from enum import IntEnum
 
 
 log = logging.getLogger(__name__)
 
 
-class TransformPen(_TransformPen):
-    def __init__(self, outPen, transformation, modified=None):
-        super(TransformPen, self).__init__(outPen, transformation)
+class TransformPointPen(_TransformPointPen):
+    def __init__(self, outPointPen, transformation, modified=None):
+        super().__init__(outPointPen, transformation)
         self.modified = modified if modified is not None else set()
         self._inverted = self._transformation.inverse()
 
-    def addComponent(self, baseGlyph, transformation):
+    def addComponent(self, baseGlyph, transformation, identifier=None, **kwargs):
         if baseGlyph in self.modified:
-
-            if transformation[:4] == (1, 0, 0, 1):
-                # if the component's transform only has a simple offset, then
-                # we don't need to transform the component again
-                self._outPen.addComponent(baseGlyph, transformation)
-                return
-
             # multiply the component's transformation matrix with the inverse
             # of the filter's transformation matrix to compensate for the
             # transformation already applied to the base glyph
             transformation = Transform(*transformation).transform(self._inverted)
 
-        super(TransformPen, self).addComponent(baseGlyph, transformation)
+        super().addComponent(baseGlyph, transformation, identifier=identifier, **kwargs)
 
 
 class TransformationsFilter(BaseFilter):
@@ -123,13 +113,13 @@ def filter(self, glyph):
                 # transformed, or there are no more components
                 modified.add(base_name)
 
-        rec = RecordingPen()
-        glyph.draw(rec)
+        rec = RecordingPointPen()
+        glyph.drawPoints(rec)
         glyph.clearContours()
         glyph.clearComponents()
 
-        outpen = glyph.getPen()
-        filterpen = TransformPen(outpen, matrix, modified)
+        outpen = glyph.getPointPen()
+        filterpen = TransformPointPen(outpen, matrix, modified)
         rec.replay(filterpen)
 
         # anchors are not drawn through the pen API,
diff --git a/tests/filters/transformations_test.py b/tests/filters/transformations_test.py
index 2815d6d8a..79d9b4424 100644
--- a/tests/filters/transformations_test.py
+++ b/tests/filters/transformations_test.py
@@ -1,7 +1,6 @@
-from __future__ import print_function, division, absolute_import
 from ufo2ft.filters.transformations import TransformationsFilter, log
 from fontTools.misc.loggingTools import CapturingLogHandler
-from fontTools.misc.py23 import isclose
+from math import isclose
 import pytest
 
 
@@ -30,6 +29,7 @@
                     "outline": [
                         ("addComponent", ("a", (1, 0, 0, 1, 0, 0))),
                         ("addComponent", ("c", (1, 0, 0, 1, 0, 0))),
+                        ("addComponent", ("a", (1, 0, 0, 1, 10, -10))),
                     ],
                 },
                 {
@@ -173,11 +173,16 @@ def test_composite_glyphs(self, font):
         assert filter_(font)
 
         b = font["b"]
-        # component 'a' was not transformed, because it doesn't have a scale
-        # or skew and the base glyph was already included
+        # component 'a' #1 was not transformed, because the base glyph was already
+        # transformed, and the component's own transformation is identity
         assert b.components[0].transformation == (1, 0, 0, 1, 0, 0)
         # component 'c' was transformed, because base glyph was not included
         assert b.components[1].transformation == (0.5, 0, 0, 0.5, -10, 51)
+        # component 'a' #2 was partly transformed: the base glyph was transformed, but
+        # the component's original transformation was not identity; thus
+        # it was modified to compensate for the transformation already applied to
+        # the base glyph (scale stays same, offsets are scaled)
+        assert b.components[2].transformation == (1, 0, 0, 1, 5, -5)
 
         d = font["d"]
         # component 'b' was transformed as well as its base glyph, because