diff --git a/src/hb-buffer-private.hh b/src/hb-buffer-private.hh
index 97bdc1be3..fa5ca166d 100644
--- a/src/hb-buffer-private.hh
+++ b/src/hb-buffer-private.hh
@@ -69,6 +69,7 @@ enum hb_buffer_scratch_flags_t {
   HB_BUFFER_SCRATCH_FLAG_HAS_SPACE_FALLBACK		= 0x00000004u,
   HB_BUFFER_SCRATCH_FLAG_HAS_GPOS_ATTACHMENT		= 0x00000008u,
   HB_BUFFER_SCRATCH_FLAG_HAS_UNSAFE_TO_BREAK		= 0x00000010u,
+  HB_BUFFER_SCRATCH_FLAG_HAS_CGJ			= 0x00000020u,
 
   /* Reserved for complex shapers' internal use. */
   HB_BUFFER_SCRATCH_FLAG_COMPLEX0			= 0x01000000u,
diff --git a/src/hb-ot-layout-private.hh b/src/hb-ot-layout-private.hh
index 0f0926f89..be5695d98 100644
--- a/src/hb-ot-layout-private.hh
+++ b/src/hb-ot-layout-private.hh
@@ -280,7 +280,11 @@ _hb_glyph_info_set_unicode_props (hb_glyph_info_t *info, hb_buffer_t *buffer)
       else if (unlikely (hb_in_range (u, 0xE0020u, 0xE007Fu))) props |= UPROPS_MASK_HIDDEN;
       /* COMBINING GRAPHEME JOINER should not be skipped; at least some times.
        * https://github.com/harfbuzz/harfbuzz/issues/554 */
-      else if (unlikely (u == 0x034Fu)) props |= UPROPS_MASK_HIDDEN;
+      else if (unlikely (u == 0x034Fu))
+      {
+	buffer->scratch_flags |= HB_BUFFER_SCRATCH_FLAG_HAS_CGJ;
+	props |= UPROPS_MASK_HIDDEN;
+      }
     }
     else if (unlikely (HB_UNICODE_GENERAL_CATEGORY_IS_NON_ENCLOSING_MARK_OR_MODIFIER_SYMBOL (gen_cat)))
     {
@@ -388,6 +392,11 @@ _hb_glyph_info_is_default_ignorable_and_not_hidden (const hb_glyph_info_t *info)
 	  == UPROPS_MASK_IGNORABLE) &&
 	 !_hb_glyph_info_ligated (info);
 }
+static inline void
+_hb_glyph_info_unhide (hb_glyph_info_t *info)
+{
+  info->unicode_props() &= ~ UPROPS_MASK_HIDDEN;
+}
 
 static inline bool
 _hb_glyph_info_is_unicode_format (const hb_glyph_info_t *info)
diff --git a/src/hb-ot-shape-complex-arabic.cc b/src/hb-ot-shape-complex-arabic.cc
index eb9d36ff1..47961bfd5 100644
--- a/src/hb-ot-shape-complex-arabic.cc
+++ b/src/hb-ot-shape-complex-arabic.cc
@@ -644,13 +644,15 @@ reorder_marks_arabic (const hb_ot_shape_plan_t *plan,
 {
   hb_glyph_info_t *info = buffer->info;
 
+  DEBUG_MSG (ARABIC, buffer, "Reordering marks from %d to %d", start, end);
+
   unsigned int i = start;
   for (unsigned int cc = 220; cc <= 230; cc += 10)
   {
-    DEBUG_MSG (ARABIC, buffer, "Looking for %d's starting at %d\n", cc, i);
+    DEBUG_MSG (ARABIC, buffer, "Looking for %d's starting at %d", cc, i);
     while (i < end && info_cc(info[i]) < cc)
       i++;
-    DEBUG_MSG (ARABIC, buffer, "Looking for %d's stopped at %d\n", cc, i);
+    DEBUG_MSG (ARABIC, buffer, "Looking for %d's stopped at %d", cc, i);
 
     if (i == end)
       break;
@@ -658,20 +660,17 @@ reorder_marks_arabic (const hb_ot_shape_plan_t *plan,
     if (info_cc(info[i]) > cc)
       continue;
 
-    /* Technically we should also check "info_cc(info[j]) == cc"
-     * in the following loop.  But not doing it is safe; we might
-     * end up moving all the 220 MCMs and 230 MCMs together in one
-     * move and be done. */
     unsigned int j = i;
-    while (j < end && info_is_mcm (info[j]))
+    while (j < end && info_cc(info[j]) == cc && info_is_mcm (info[j]))
       j++;
-    DEBUG_MSG (ARABIC, buffer, "Found %d's from %d to %d\n", cc, i, j);
 
     if (i == j)
       continue;
 
+    DEBUG_MSG (ARABIC, buffer, "Found %d's from %d to %d", cc, i, j);
+
     /* Shift it! */
-    DEBUG_MSG (ARABIC, buffer, "Shifting %d's: %d %d\n", cc, i, j);
+    DEBUG_MSG (ARABIC, buffer, "Shifting %d's: %d %d", cc, i, j);
     hb_glyph_info_t temp[HB_OT_SHAPE_COMPLEX_MAX_COMBINING_MARKS];
     assert (j - i <= ARRAY_LENGTH (temp));
     buffer->merge_clusters (start, j);
@@ -679,7 +678,25 @@ reorder_marks_arabic (const hb_ot_shape_plan_t *plan,
     memmove (&info[start + j - i], &info[start], (i - start) * sizeof (hb_glyph_info_t));
     memmove (&info[start], temp, (j - i) * sizeof (hb_glyph_info_t));
 
-    start += j - i;
+    /* Renumber CC such that the reordered sequence is still sorted.
+     * 22 and 26 are chosen because they are smaller than all Arabic categories,
+     * and are folded back to 220/230 respectively during fallback mark positioning.
+     *
+     * We do this because the CGJ-handling logic in the normalizer relies on
+     * mark sequences having an increasing order even after this reordering.
+     * https://github.com/harfbuzz/harfbuzz/issues/554
+     * This, however, does break some obscure sequences, where the normalizer
+     * might compose a sequence that it should not.  For example, in the seequence
+     * ALEF, HAMZAH, MADDAH, we should NOT try to compose ALEF+MADDAH, but with this
+     * renumbering, we will.
+     */
+    unsigned int new_start = start + j - i;
+    unsigned int new_cc = cc == 220 ? HB_MODIFIED_COMBINING_CLASS_CCC22 : HB_MODIFIED_COMBINING_CLASS_CCC26;
+    while (start < new_start)
+    {
+      _hb_glyph_info_set_modified_combining_class (&info[start], new_cc);
+      start++;
+    }
 
     i = j;
   }
diff --git a/src/hb-ot-shape-normalize.cc b/src/hb-ot-shape-normalize.cc
index fd9e7c2a8..62cbb9de9 100644
--- a/src/hb-ot-shape-normalize.cc
+++ b/src/hb-ot-shape-normalize.cc
@@ -345,9 +345,8 @@ _hb_ot_shape_normalize (const hb_ot_shape_plan_t *plan,
       if (_hb_glyph_info_get_modified_combining_class (&buffer->info[end]) == 0)
         break;
 
-    /* We are going to do a O(n^2).  Only do this if the sequence is short,
-     * but not too short ;). */
-    if (end - i < 2 || end - i > HB_OT_SHAPE_COMPLEX_MAX_COMBINING_MARKS) {
+    /* We are going to do a O(n^2).  Only do this if the sequence is short. */
+    if (end - i > HB_OT_SHAPE_COMPLEX_MAX_COMBINING_MARKS) {
       i = end;
       continue;
     }
@@ -373,13 +372,11 @@ _hb_ot_shape_normalize (const hb_ot_shape_plan_t *plan,
   buffer->clear_output ();
   count = buffer->len;
   unsigned int starter = 0;
-  bool combine = true;
   buffer->next_glyph ();
   while (buffer->idx < count && !buffer->in_error)
   {
     hb_codepoint_t composed, glyph;
-    if (combine &&
-	/* We don't try to compose a non-mark character with it's preceding starter.
+    if (/* We don't try to compose a non-mark character with it's preceding starter.
 	 * This is both an optimization to avoid trying to compose every two neighboring
 	 * glyphs in most scripts AND a desired feature for Hangul.  Apparently Hangul
 	 * fonts are not designed to mix-and-match pre-composed syllables and Jamo. */
@@ -410,22 +407,27 @@ _hb_ot_shape_normalize (const hb_ot_shape_plan_t *plan,
 
 	continue;
       }
-      else if (/* We sometimes custom-tailor the sorted order of marks. In that case, stop
-		* trying to combine as soon as combining-class drops. */
-	       starter < buffer->out_len - 1 &&
-	       info_cc (buffer->prev()) > info_cc (buffer->cur()))
-        combine = false;
     }
 
     /* Blocked, or doesn't compose. */
     buffer->next_glyph ();
 
     if (info_cc (buffer->prev()) == 0)
-    {
       starter = buffer->out_len - 1;
-      combine = true;
-    }
   }
   buffer->swap_buffers ();
 
+  if (buffer->scratch_flags & HB_BUFFER_SCRATCH_FLAG_HAS_CGJ)
+  {
+    /* For all CGJ, check if it prevented any reordering at all.
+     * If it did NOT, then make it skippable.
+     * https://github.com/harfbuzz/harfbuzz/issues/554
+     */
+    for (unsigned int i = 1; i + 1 < buffer->len; i++)
+      if (buffer->info[i].codepoint == 0x034Fu/*CGJ*/ &&
+	  info_cc(buffer->info[i-1]) <= info_cc(buffer->info[i+1]))
+      {
+	_hb_glyph_info_unhide (&buffer->info[i]);
+      }
+  }
 }
diff --git a/test/shaping/tests/arabic-mark-order.tests b/test/shaping/tests/arabic-mark-order.tests
index b48c82fd3..cc5226bb2 100644
--- a/test/shaping/tests/arabic-mark-order.tests
+++ b/test/shaping/tests/arabic-mark-order.tests
@@ -1,2 +1,6 @@
 fonts/sha1sum/94a5d6fb15a27521fba9ea4aee9cb39b2d03322a.ttf::U+064A,U+064E,U+0670,U+0653,U+0640,U+0654,U+064E,U+0627:[afii57415.zz04=7+481|afii57454=4@25,975+0|uni0654=4@-50,50+0|afii57440=4+650|uni0670_uni0653=0@75,400+0|afii57454=0@750,1125+0|afii57450.calt=0+1331]
 fonts/sha1sum/24b8d24d00ae86f49791b746da4c9d3f717a51a8.ttf::U+0628,U+0618,U+0619,U+064E,U+064F,U+0654,U+0658,U+0653,U+0654,U+0651,U+0656,U+0651,U+065C,U+0655,U+0650:[uni0653.small=0@266,2508+0|uni0654=0@308,2151+0|uni0655=0@518,-1544+0|uni065C=0@501,-1453+0|uni0656=0@573,-659+0|uni0650=0@500,133+0|uni0619=0@300,1807+0|uni0618=0@357,1674+0|uni0651064E=0@387,1178+0|uni0651=0@402,764+0|uni0658=0@424,404+0|uni0654064F=0@540,-435+0|uni0628=0+1352]
+fonts/sha1sum/21b7fb9c1eeae260473809fbc1fe330f66a507cd.ttf::U+0649,U+0655,U+034F,U+0650:[uni0650.small2=0@727,-774+0|space=0+0|uni0655=0@727,-209+0|uni0649=0+1566]
+fonts/sha1sum/21b7fb9c1eeae260473809fbc1fe330f66a507cd.ttf::U+0649,U+0655,U+0650:[uni0650.small2=0@727,-774+0|uni0655=0@727,-209+0|uni0649=0+1566]
+fonts/sha1sum/21b7fb9c1eeae260473809fbc1fe330f66a507cd.ttf::U+0649,U+0650,U+0655:[uni0650.small2=0@727,-774+0|uni0655=0@727,-209+0|uni0649=0+1566]
+fonts/sha1sum/21b7fb9c1eeae260473809fbc1fe330f66a507cd.ttf::U+0649,U+0650,U+034F,U+0655:[uni0655=0+0|space=0+0|uni0650=0@166,0+0|uni0649=0+1566]