diff --git a/src/OT/glyf/glyf.hh b/src/OT/glyf/glyf.hh
index 7866b70a6..d7cdc8f4c 100644
--- a/src/OT/glyf/glyf.hh
+++ b/src/OT/glyf/glyf.hh
@@ -230,8 +230,60 @@ struct glyf_accelerator_t
     if (consumer.is_consuming_contour_points ())
     {
       auto *points = all_points.arrayZ;
-      for (unsigned i = 0; i < count; i++)
-	consumer.consume_point (points[i]);
+
+      if (false)
+      {
+	/* Our path-builder was designed to work with this simple loop.
+	 * But FreeType and CoreText do it differently, so we match those
+	 * with the other, more complicated, code branch below. */
+	for (unsigned i = 0; i < count; i++)
+	{
+	  consumer.consume_point (points[i]);
+	  if (points[i].is_end_point)
+	    consumer.contour_end ();
+	}
+      }
+      else
+      {
+	for (unsigned i = 0; i < count; i++)
+	{
+	  // Start of a contour.
+	  if (points[i].flag & glyf_impl::SimpleGlyph::FLAG_ON_CURVE)
+	  {
+	    // First point is on-curve. Draw the contour.
+	    for (; i < count; i++)
+	    {
+	      consumer.consume_point (points[i]);
+	      if (points[i].is_end_point)
+	      {
+		consumer.contour_end ();
+		break;
+	      }
+	    }
+	  }
+	  else
+	  {
+	    unsigned start = i;
+
+	    // Find end of the contour.
+	    for (; i < count; i++)
+	      if (points[i].is_end_point)
+		break;
+
+	    unsigned end = i;
+
+	    // Enough to start from the end. Our path-builder takes care of the rest.
+	    if (likely (end < count)) // Can only fail in case of alloc failure *maybe*.
+	      consumer.consume_point (points[end]);
+
+	    for (i = start; i < end; i++)
+	      consumer.consume_point (points[i]);
+
+	    consumer.contour_end ();
+	  }
+	}
+      }
+
       consumer.points_end ();
     }
 
@@ -304,6 +356,7 @@ struct glyf_accelerator_t
 
     HB_ALWAYS_INLINE
     void consume_point (const contour_point_t &point) { bounds.add (point); }
+    void contour_end () {}
     void points_end () { bounds.get_extents (font, extents, scaled); }
 
     bool is_consuming_contour_points () { return extents; }
diff --git a/src/OT/glyf/path-builder.hh b/src/OT/glyf/path-builder.hh
index f55052450..db9efa945 100644
--- a/src/OT/glyf/path-builder.hh
+++ b/src/OT/glyf/path-builder.hh
@@ -124,58 +124,60 @@ struct path_builder_t
       }
     }
 
-    if (unlikely (point.is_end_point))
-    {
-      if (first_offcurve && last_offcurve)
-      {
-	optional_point_t mid = last_offcurve.mid (first_offcurve2 ?
-						  first_offcurve2 :
-						  first_offcurve);
-	if (last_offcurve2)
-	  draw_session->cubic_to (last_offcurve2.x, last_offcurve2.y,
-				  last_offcurve.x, last_offcurve.y,
-				  mid.x, mid.y);
-	else
-	  draw_session->quadratic_to (last_offcurve.x, last_offcurve.y,
-				     mid.x, mid.y);
-	last_offcurve = optional_point_t ();
-      }
-      /* now check the rest */
-
-      if (first_offcurve && first_oncurve)
-      {
-        if (first_offcurve2)
-	  draw_session->cubic_to (first_offcurve2.x, first_offcurve2.y,
-				  first_offcurve.x, first_offcurve.y,
-				  first_oncurve.x, first_oncurve.y);
-	else
-	  draw_session->quadratic_to (first_offcurve.x, first_offcurve.y,
-				     first_oncurve.x, first_oncurve.y);
-      }
-      else if (last_offcurve && first_oncurve)
-      {
-	if (last_offcurve2)
-	  draw_session->cubic_to (last_offcurve2.x, last_offcurve2.y,
-				  last_offcurve.x, last_offcurve.y,
-				  first_oncurve.x, first_oncurve.y);
-	else
-	  draw_session->quadratic_to (last_offcurve.x, last_offcurve.y,
-				     first_oncurve.x, first_oncurve.y);
-      }
-      else if (first_oncurve)
-	draw_session->line_to (first_oncurve.x, first_oncurve.y);
-      else if (first_offcurve)
-      {
-	float x = first_offcurve.x, y = first_offcurve.y;
-	draw_session->move_to (x, y);
-	draw_session->quadratic_to (x, y, x, y);
-      }
-
-      /* Getting ready for the next contour */
-      first_oncurve = first_offcurve = last_offcurve = last_offcurve2 = optional_point_t ();
-      draw_session->close_path ();
-    }
   }
+
+  void contour_end ()
+  {
+    if (first_offcurve && last_offcurve)
+    {
+      optional_point_t mid = last_offcurve.mid (first_offcurve2 ?
+						first_offcurve2 :
+						first_offcurve);
+      if (last_offcurve2)
+	draw_session->cubic_to (last_offcurve2.x, last_offcurve2.y,
+				last_offcurve.x, last_offcurve.y,
+				mid.x, mid.y);
+      else
+	draw_session->quadratic_to (last_offcurve.x, last_offcurve.y,
+				   mid.x, mid.y);
+      last_offcurve = optional_point_t ();
+    }
+    /* now check the rest */
+
+    if (first_offcurve && first_oncurve)
+    {
+      if (first_offcurve2)
+	draw_session->cubic_to (first_offcurve2.x, first_offcurve2.y,
+				first_offcurve.x, first_offcurve.y,
+				first_oncurve.x, first_oncurve.y);
+      else
+	draw_session->quadratic_to (first_offcurve.x, first_offcurve.y,
+				   first_oncurve.x, first_oncurve.y);
+    }
+    else if (last_offcurve && first_oncurve)
+    {
+      if (last_offcurve2)
+	draw_session->cubic_to (last_offcurve2.x, last_offcurve2.y,
+				last_offcurve.x, last_offcurve.y,
+				first_oncurve.x, first_oncurve.y);
+      else
+	draw_session->quadratic_to (last_offcurve.x, last_offcurve.y,
+				   first_oncurve.x, first_oncurve.y);
+    }
+    else if (first_oncurve)
+      draw_session->line_to (first_oncurve.x, first_oncurve.y);
+    else if (first_offcurve)
+    {
+      float x = first_offcurve.x, y = first_offcurve.y;
+      draw_session->move_to (x, y);
+      draw_session->quadratic_to (x, y, x, y);
+    }
+
+    /* Getting ready for the next contour */
+    first_oncurve = first_offcurve = last_offcurve = last_offcurve2 = optional_point_t ();
+    draw_session->close_path ();
+  }
+
   void points_end () {}
 
   bool is_consuming_contour_points () { return true; }