diff --git a/Lib/fontTools/ttLib/tables/_g_l_y_f.py b/Lib/fontTools/ttLib/tables/_g_l_y_f.py
index 46c5dca50..341c4ed64 100644
--- a/Lib/fontTools/ttLib/tables/_g_l_y_f.py
+++ b/Lib/fontTools/ttLib/tables/_g_l_y_f.py
@@ -1528,9 +1528,15 @@ class Glyph(object):
             start = end
             pen.beginPath()
             # Start with the appropriate segment type based on the final segment
-            segmentType = "line" if cFlags[-1] == 1 else "qcurve"
+
+            if cFlags[-1] & flagOnCurve:
+                segmentType = "line"
+            elif cFlags[-1] & flagCubic:
+                segmentType = "curve"
+            else:
+                segmentType = "qcurve"
             for i, pt in enumerate(contour):
-                if cFlags[i] & flagOnCurve == 1:
+                if cFlags[i] & flagOnCurve:
                     pen.addPoint(pt, segmentType=segmentType)
                     segmentType = "line"
                 else:
diff --git a/Tests/ttLib/ttGlyphSet_test.py b/Tests/ttLib/ttGlyphSet_test.py
index 3a4d9a937..1b31d229a 100644
--- a/Tests/ttLib/ttGlyphSet_test.py
+++ b/Tests/ttLib/ttGlyphSet_test.py
@@ -563,14 +563,68 @@ class TTGlyphSetTest(object):
         glyphset["one"].draw(pen)
         assert pen.value == expected
 
+        expectedPoints = [
+            ("beginPath", (), {}),
+            ("addPoint", ((76, 181), "curve", False, None), {}),
+            ("addPoint", ((103, 181), None, False, None), {}),
+            ("addPoint", ((125, 158), None, False, None), {}),
+            ("addPoint", ((125, 104), None, False, None), {}),
+            ("addPoint", ((103, 82), None, False, None), {}),
+            ("addPoint", ((76, 82), "curve", False, None), {}),
+            ("addPoint", ((48, 82), None, False, None), {}),
+            ("addPoint", ((26, 104), None, False, None), {}),
+            ("addPoint", ((26, 158), None, False, None), {}),
+            ("addPoint", ((48, 181), None, False, None), {}),
+            ("endPath", (), {}),
+        ]
+        pen = RecordingPointPen()
+        glyphset["one"].drawPoints(pen)
+        assert pen.value == expectedPoints
+
         pen = RecordingPen()
         glyphset["two"].draw(pen)
         assert pen.value == expected
 
+        expectedPoints = [
+            ("beginPath", (), {}),
+            ("addPoint", ((26, 158), None, False, None), {}),
+            ("addPoint", ((48, 181), None, False, None), {}),
+            ("addPoint", ((76, 181), "curve", False, None), {}),
+            ("addPoint", ((103, 181), None, False, None), {}),
+            ("addPoint", ((125, 158), None, False, None), {}),
+            ("addPoint", ((125, 104), None, False, None), {}),
+            ("addPoint", ((103, 82), None, False, None), {}),
+            ("addPoint", ((76, 82), "curve", False, None), {}),
+            ("addPoint", ((48, 82), None, False, None), {}),
+            ("addPoint", ((26, 104), None, False, None), {}),
+            ("endPath", (), {}),
+        ]
+        pen = RecordingPointPen()
+        glyphset["two"].drawPoints(pen)
+        assert pen.value == expectedPoints
+
         pen = RecordingPen()
         glyphset["three"].draw(pen)
         assert pen.value == expected
 
+        expectedPoints = [
+            ("beginPath", (), {}),
+            ("addPoint", ((48, 82), None, False, None), {}),
+            ("addPoint", ((26, 104), None, False, None), {}),
+            ("addPoint", ((26, 158), None, False, None), {}),
+            ("addPoint", ((48, 181), None, False, None), {}),
+            ("addPoint", ((76, 181), "curve", False, None), {}),
+            ("addPoint", ((103, 181), None, False, None), {}),
+            ("addPoint", ((125, 158), None, False, None), {}),
+            ("addPoint", ((125, 104), None, False, None), {}),
+            ("addPoint", ((103, 82), None, False, None), {}),
+            ("addPoint", ((76, 82), "curve", False, None), {}),
+            ("endPath", (), {}),
+        ]
+        pen = RecordingPointPen()
+        glyphset["three"].drawPoints(pen)
+        assert pen.value == expectedPoints
+
         pen = RecordingPen()
         glyphset["four"].draw(pen)
         assert pen.value == [
@@ -581,3 +635,21 @@ class TTGlyphSetTest(object):
             ("curveTo", ((26, 158), (48, 181), (75.5, 181))),
             ("closePath", ()),
         ]
+
+        # Ouch! We can't represent all-cubic-offcurves in pointPen!
+        expectedPoints = [
+            ("beginPath", (), {}),
+            ("addPoint", ((103, 181), None, False, None), {}),
+            ("addPoint", ((125, 158), None, False, None), {}),
+            ("addPoint", ((125, 104), None, False, None), {}),
+            ("addPoint", ((103, 82), None, False, None), {}),
+            ("addPoint", ((48, 82), None, False, None), {}),
+            ("addPoint", ((26, 104), None, False, None), {}),
+            ("addPoint", ((26, 158), None, False, None), {}),
+            ("addPoint", ((48, 181), None, False, None), {}),
+            ("endPath", (), {}),
+        ]
+        pen = RecordingPointPen()
+        glyphset["four"].drawPoints(pen)
+        print(pen.value)
+        assert pen.value == expectedPoints