diff --git a/src/hb-draw.hh b/src/hb-draw.hh
index 03b518ed6..f0655b7fd 100644
--- a/src/hb-draw.hh
+++ b/src/hb-draw.hh
@@ -59,6 +59,7 @@ struct draw_helper_t
 
   void line_to (hb_position_t x, hb_position_t y)
   {
+    if (equal_to_current (x, y)) return;
     if (!path_open) start_path ();
     funcs->line_to (x, y, user_data);
     current_x = x;
@@ -69,6 +70,8 @@ struct draw_helper_t
   quadratic_to (hb_position_t control_x, hb_position_t control_y,
 		hb_position_t to_x, hb_position_t to_y)
   {
+    if (equal_to_current (control_x, control_y) && equal_to_current (to_x, to_y))
+      return;
     if (!path_open) start_path ();
     if (funcs->is_quadratic_to_set)
       funcs->quadratic_to (control_x, control_y, to_x, to_y, user_data);
@@ -83,14 +86,18 @@ struct draw_helper_t
   }
 
   void
-  cubic_to (hb_position_t x1, hb_position_t y1,
-	    hb_position_t x2, hb_position_t y2,
-	    hb_position_t x3, hb_position_t y3)
+  cubic_to (hb_position_t control1_x, hb_position_t control1_y,
+	    hb_position_t control2_x, hb_position_t control2_y,
+	    hb_position_t to_x, hb_position_t to_y)
   {
+    if (equal_to_current (control1_x, control1_y) &&
+        equal_to_current (control2_x, control2_y) &&
+	equal_to_current (to_x, to_y))
+      return;
     if (!path_open) start_path ();
-    funcs->cubic_to (x1, y1, x2, y2, x3, y3, user_data);
-    current_x = x3;
-    current_y = y3;
+    funcs->cubic_to (control1_x, control1_y, control2_x, control2_y, to_x, to_y, user_data);
+    current_x = to_x;
+    current_y = to_y;
   }
 
   void end_path ()
@@ -106,6 +113,9 @@ struct draw_helper_t
   }
 
   protected:
+  bool equal_to_current (hb_position_t x, hb_position_t y)
+  { return current_x == x && current_y == y; }
+
   void start_path ()
   {
     if (path_open) end_path ();
diff --git a/test/api/test-draw.c b/test/api/test-draw.c
index 903fd8aeb..df6c27658 100644
--- a/test/api/test-draw.c
+++ b/test/api/test-draw.c
@@ -769,8 +769,8 @@ test_hb_draw_stroking (void)
 
     user_data.consumed = 0;
     g_assert (hb_font_draw_glyph (font, 6, funcs, &user_data));
-    char expected[] = "M1626,1522Q1626,1522 1626,1522Q1626,1522 1626,1522ZM436,1522"
-		      "Q436,1280 531,1060Q625,839 784,680Q943,521 1164,427Q1384,332 1626,332"
+    /* Skip empty path where all the points of a path are equal */
+    char expected[] = "M436,1522Q436,1280 531,1060Q625,839 784,680Q943,521 1164,427Q1384,332 1626,332"
 		      "Q1868,332 2089,427Q2309,521 2468,680Q2627,839 2722,1060Q2816,1280 2816,1522"
 		      "Q2816,1764 2722,1985Q2627,2205 2468,2364Q2309,2523 2089,2618Q1868,2712 1626,2712"
 		      "Q1384,2712 1164,2618Q943,2523 784,2364Q625,2205 531,1985Q436,1764 436,1522ZM256,1528"
@@ -810,8 +810,8 @@ test_hb_draw_stroking (void)
 
     user_data.consumed = 0;
     g_assert (hb_font_draw_glyph (font, 4, funcs, &user_data));
-    char expected[] = "M397,372L397,372Z" /* TODO: Do we like to fold this path? */
-		      "M106,372C106,532 237,662 397,662C557,662 688,532 688,372C688,212 557,81 397,81C237,81 106,212 106,372Z"
+    /* Skip empty path in CFF */
+    char expected[] = "M106,372C106,532 237,662 397,662C557,662 688,532 688,372C688,212 557,81 397,81C237,81 106,212 106,372Z"
 		      "M62,373C62,188 212,39 397,39C582,39 731,188 731,373C731,558 582,708 397,708C212,708 62,558 62,373Z";
     g_assert_cmpmem (str, user_data.consumed, expected, sizeof (expected) - 1);
 
diff --git a/test/fuzzing/hb-draw-fuzzer.cc b/test/fuzzing/hb-draw-fuzzer.cc
index e35c15e06..25fe66da6 100644
--- a/test/fuzzing/hb-draw-fuzzer.cc
+++ b/test/fuzzing/hb-draw-fuzzer.cc
@@ -36,17 +36,20 @@ _line_to (hb_position_t to_x, hb_position_t to_y, void *user_data_)
 {
   _user_data_t *user_data = (_user_data_t *) user_data_;
   assert (user_data->is_open);
+  assert (user_data->path_last_x != to_x || user_data->path_last_y != to_y);
   ++user_data->path_len;
   user_data->path_last_x = to_x;
   user_data->path_last_y = to_y;
 }
 
 static void
-_quadratic_to (hb_position_t control_x HB_UNUSED, hb_position_t control_y HB_UNUSED,
+_quadratic_to (hb_position_t control_x, hb_position_t control_y,
 	       hb_position_t to_x, hb_position_t to_y, void *user_data_)
 {
   _user_data_t *user_data = (_user_data_t *) user_data_;
   assert (user_data->is_open);
+  assert (user_data->path_last_x != control_x || user_data->path_last_y != control_y ||
+	  user_data->path_last_x != to_x || user_data->path_last_y != to_y);
   ++user_data->path_len;
   user_data->path_last_x = to_x;
   user_data->path_last_y = to_y;
@@ -59,6 +62,9 @@ _cubic_to (hb_position_t control1_x HB_UNUSED, hb_position_t control1_y HB_UNUSE
 {
   _user_data_t *user_data = (_user_data_t *) user_data_;
   assert (user_data->is_open);
+  assert (user_data->path_last_x != control1_x || user_data->path_last_y != control1_y ||
+	  user_data->path_last_x != control2_x || user_data->path_last_y != control2_y ||
+	  user_data->path_last_x != to_x || user_data->path_last_y != to_y);
   ++user_data->path_len;
   user_data->path_last_x = to_x;
   user_data->path_last_y = to_y;