diff --git a/src/hb-iter.hh b/src/hb-iter.hh
index 94fd8a0f9..ad2e45e3c 100644
--- a/src/hb-iter.hh
+++ b/src/hb-iter.hh
@@ -607,9 +607,10 @@ struct hb_concat_iter_t :
 
   __item_t__ __item_at__ (unsigned i) const
   {
-    if (i < a.len())
+    unsigned a_len = a.len ();
+    if (i < a_len)
       return a[i];
-    return b[i - a.len()];
+    return b[i - a_len];
   }
 
   bool __more__ () const { return bool (a) || bool (b); }
@@ -626,9 +627,18 @@ struct hb_concat_iter_t :
 
   void __forward__ (unsigned n)
   {
-    if (n > a.len ()) {
-      n -= a.len ();
-      a.__forward__ (a.len ());
+    if (!n) return;
+    if (!is_random_access_iterator) {
+      while (n-- && *this) {
+        (*this)++;
+      }
+      return;
+    }
+
+    unsigned a_len = a.len ();
+    if (n > a_len) {
+      n -= a_len;
+      a.__forward__ (a_len);
       b.__forward__ (n);
     } else {
       a.__forward__ (n);
diff --git a/src/test-iter.cc b/src/test-iter.cc
index 6182eb1e8..dc85b7214 100644
--- a/src/test-iter.cc
+++ b/src/test-iter.cc
@@ -133,6 +133,7 @@ static void test_concat ()
 
   auto it1 = hb_concat (a, b);
   assert (it1.len () == 5);
+  assert (it1.is_random_access_iterator);
   auto it2 = hb_concat (c, d);
   assert (it2.len () == 5);
   auto it3 = hb_concat (d, c);
@@ -148,6 +149,9 @@ static void test_concat ()
   check_sequential (it3);
 
   auto it4 = +it1;
+  it4 += 0;
+  assert (*it4 == 1);
+
   it4 += 2;
   assert (*it4 == 3);
   assert (it4);
@@ -165,6 +169,21 @@ static void test_concat ()
   auto it5 = +it1;
   it5 += 3;
   assert (*it5 == 4);
+
+  hb_set_t s_a = {1, 2, 3};
+  hb_set_t s_b = {4, 5};
+  auto it6 = hb_concat (s_a, s_b);
+  assert (!it6.is_random_access_iterator);
+  check_sequential (it6);
+  assert (it6.len () == 5);
+
+  it6 += 0;
+  assert (*it6 == 1);
+
+  it6 += 3;
+  assert (*it6 == 4);
+  assert (it6);
+  assert (it6.len () == 2);
 }
 
 int