diff --git a/src/OT/glyf/SimpleGlyph.hh b/src/OT/glyf/SimpleGlyph.hh
index 9927f5301..b6fefce1a 100644
--- a/src/OT/glyf/SimpleGlyph.hh
+++ b/src/OT/glyf/SimpleGlyph.hh
@@ -20,7 +20,7 @@ struct SimpleGlyph
     FLAG_X_SAME         = 0x10,
     FLAG_Y_SAME         = 0x20,
     FLAG_OVERLAP_SIMPLE = 0x40,
-    FLAG_RESERVED2      = 0x80
+    FLAG_CUBIC          = 0x80
   };
 
   const GlyphHeader &header;
diff --git a/src/OT/glyf/path-builder.hh b/src/OT/glyf/path-builder.hh
index 9bfc45a1a..0b2b913c1 100644
--- a/src/OT/glyf/path-builder.hh
+++ b/src/OT/glyf/path-builder.hh
@@ -26,13 +26,13 @@ struct path_builder_t
 
     optional_point_t lerp (optional_point_t p, float t)
     { return optional_point_t (x + t * (p.x - x), y + t * (p.y - y)); }
-  } first_oncurve, first_offcurve, last_offcurve;
+  } first_oncurve, first_offcurve, last_offcurve, last_offcurve2;
 
   path_builder_t (hb_font_t *font_, hb_draw_session_t &draw_session_)
   {
     font = font_;
     draw_session = &draw_session_;
-    first_oncurve = first_offcurve = last_offcurve = optional_point_t ();
+    first_oncurve = first_offcurve = last_offcurve = last_offcurve2 = optional_point_t ();
   }
 
   /* based on https://github.com/RazrFalcon/ttf-parser/blob/4f32821/src/glyf.rs#L287
@@ -42,6 +42,7 @@ struct path_builder_t
   void consume_point (const contour_point_t &point)
   {
     bool is_on_curve = point.flag & glyf_impl::SimpleGlyph::FLAG_ON_CURVE;
+    bool is_cubic = !is_on_curve && (point.flag & glyf_impl::SimpleGlyph::FLAG_CUBIC);
     optional_point_t p (font->em_fscalef_x (point.x), font->em_fscalef_y (point.y));
     if (!first_oncurve)
     {
@@ -69,16 +70,41 @@ struct path_builder_t
       {
 	if (is_on_curve)
 	{
-	  draw_session->quadratic_to (last_offcurve.x, last_offcurve.y,
-				     p.x, p.y);
+	  if (last_offcurve2)
+	  {
+	    draw_session->cubic_to (last_offcurve2.x, last_offcurve2.y,
+				    last_offcurve.x, last_offcurve.y,
+				    p.x, p.y);
+	    last_offcurve2 = optional_point_t ();
+	  }
+	  else
+	    draw_session->quadratic_to (last_offcurve.x, last_offcurve.y,
+				       p.x, p.y);
 	  last_offcurve = optional_point_t ();
 	}
 	else
 	{
-	  optional_point_t mid = last_offcurve.lerp (p, .5f);
-	  draw_session->quadratic_to (last_offcurve.x, last_offcurve.y,
-				     mid.x, mid.y);
-	  last_offcurve = p;
+	  if (is_cubic && !last_offcurve2)
+	  {
+	    last_offcurve2 = last_offcurve;
+	    last_offcurve = p;
+	  }
+	  else
+	  {
+	    optional_point_t mid = last_offcurve.lerp (p, .5f);
+
+	    if (is_cubic)
+	    {
+	      draw_session->cubic_to (last_offcurve2.x, last_offcurve2.y,
+				      last_offcurve.x, last_offcurve.y,
+				      mid.x, mid.y);
+	      last_offcurve2 = optional_point_t ();
+	    }
+	    else
+	      draw_session->quadratic_to (last_offcurve.x, last_offcurve.y,
+					 mid.x, mid.y);
+	    last_offcurve = p;
+	  }
 	}
       }
       else
@@ -105,8 +131,15 @@ struct path_builder_t
 	draw_session->quadratic_to (first_offcurve.x, first_offcurve.y,
 				   first_oncurve.x, first_oncurve.y);
       else if (last_offcurve && first_oncurve)
-	draw_session->quadratic_to (last_offcurve.x, last_offcurve.y,
-				   first_oncurve.x, first_oncurve.y);
+      {
+	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)
@@ -117,7 +150,7 @@ struct path_builder_t
       }
 
       /* Getting ready for the next contour */
-      first_oncurve = first_offcurve = last_offcurve = optional_point_t ();
+      first_oncurve = first_offcurve = last_offcurve = last_offcurve2 = optional_point_t ();
       draw_session->close_path ();
     }
   }