diff --git a/benchtests/bench-memcpy-random.c b/benchtests/bench-memcpy-random.c
index c490b73ed0..eeeef42fc1 100644
--- a/benchtests/bench-memcpy-random.c
+++ b/benchtests/bench-memcpy-random.c
@@ -16,7 +16,8 @@
    License along with the GNU C Library; if not, see
    <https://www.gnu.org/licenses/>.  */
 
-#define MIN_PAGE_SIZE (512*1024+getpagesize())
+#define MAX_TEST_SIZE (512*1024)
+#define MIN_PAGE_SIZE (3*MAX_TEST_SIZE+getpagesize())
 #define TEST_MAIN
 #define TEST_NAME "memcpy"
 #include "bench-string.h"
@@ -89,9 +90,12 @@ static align_data_t dst_align_freq[] =
 
 typedef struct
 {
-  uint64_t src : 24;
-  uint64_t dst : 24;
-  uint64_t len : 16;
+/* 26 bits for src and dst so we have extra bit for alternating dst >
+   src without a branch.  */
+  uint64_t src : 26;
+  uint64_t dst : 26;
+/* For size < 4096 12 bits is enough.  */
+  uint64_t len : 12;
 } copy_t;
 
 static copy_t copy[MAX_COPIES];
@@ -142,34 +146,100 @@ do_one_test (json_ctx_t *json_ctx, impl_t *impl, char *dst, char *src,
 }
 
 static void
-do_test (json_ctx_t *json_ctx, size_t max_size)
+do_one_fixed_test (json_ctx_t *json_ctx, impl_t *impl, char *dst, char *src,
+               copy_t *copy, size_t n, size_t size)
 {
-  int i;
+  timing_t start, stop, cur;
+  size_t iters = INNER_LOOP_ITERS_SMALL;
+
+  for (int j = 0; j < n; j++)
+    CALL (impl, dst + copy[j].dst, src + copy[j].src, size);
+
+  TIMING_NOW (start);
+  for (int i = 0; i < iters; ++i)
+    for (int j = 0; j < n; j++)
+      CALL (impl, dst + copy[j].dst, src + copy[j].src, size);
+  TIMING_NOW (stop);
+
+  TIMING_DIFF (cur, start, stop);
+
+  json_element_double (json_ctx, (double) cur / (double) iters);
+}
+
+
+static size_t
+init_copy(size_t max_size, int dst_gt_src)
+{
+  size_t i, dst_offset, src_offset;
+  if (dst_gt_src <= 0)
+    {
+      dst_offset = 0;
+      src_offset = max_size;
+    }
+  else
+    {
+      dst_offset = max_size;
+      src_offset = 0;
+    }
 
-  memset (buf1, 1, max_size);
 
   /* Create a random set of copies with the given size and alignment
      distributions.  */
   for (i = 0; i < MAX_COPIES; i++)
     {
+      dst_offset  = dst_gt_src == -1
+                        ? (rand() & 1) ? max_size : 0
+                        : dst_offset;
       copy[i].dst = (rand () & (max_size - 1));
       copy[i].dst &= ~dst_align_arr[rand () & ALIGN_MASK];
+      copy[i].dst += dst_offset;
       copy[i].src = (rand () & (max_size - 1));
       copy[i].src &= ~src_align_arr[rand () & ALIGN_MASK];
+      copy[i].src += src_offset;
       copy[i].len = size_arr[rand () & SIZE_MASK];
     }
+  memset (buf1, 1, 3 * max_size);
+  return i;
+}
+
+static void
+do_test (json_ctx_t *json_ctx, size_t max_size, int dst_gt_src)
+{
+  size_t n;
+  n = init_copy(max_size, dst_gt_src);
+  json_element_object_begin (json_ctx);
+  json_attr_uint (json_ctx, "region-size", (double) 3 * max_size);
+  json_attr_int (json_ctx, "dst > src", (double) dst_gt_src);
+  json_attr_uint (json_ctx, "with-fixed-size", (double) 0);
+  json_array_begin (json_ctx, "timings");
+
+  FOR_EACH_IMPL (impl, 0)
+    do_one_test (json_ctx, impl, (char *) buf1, (char *) buf1, copy, n);
+
+  json_array_end (json_ctx);
+  json_element_object_end (json_ctx);
+}
 
+static void
+do_test_fixed_size (json_ctx_t *json_ctx, size_t size, size_t max_size, int dst_gt_src)
+{
+  size_t n;
+  n = init_copy(3 * max_size, dst_gt_src);
   json_element_object_begin (json_ctx);
-  json_attr_uint (json_ctx, "length", (double) max_size);
+  json_attr_uint (json_ctx, "region-size", (double) 3 * max_size);
+  json_attr_int (json_ctx, "dst > src", (double) dst_gt_src);
+  json_attr_uint (json_ctx, "with-fixed-size", (double) 1);
+  json_attr_uint (json_ctx, "size", (double) size);
   json_array_begin (json_ctx, "timings");
 
   FOR_EACH_IMPL (impl, 0)
-    do_one_test (json_ctx, impl, (char *) buf2, (char *) buf1, copy, i);
+    do_one_fixed_test (json_ctx, impl, (char *) buf1, (char *) buf1, copy, n, size);
 
   json_array_end (json_ctx);
   json_element_object_end (json_ctx);
 }
 
+
 int
 test_main (void)
 {
@@ -193,8 +263,19 @@ test_main (void)
   json_array_end (&json_ctx);
 
   json_array_begin (&json_ctx, "results");
-  for (int i = 4; i <= 512; i = i * 2)
-    do_test (&json_ctx, i * 1024);
+  for (int i = 4096; i < MAX_TEST_SIZE; i = i * 2)
+    {
+      do_test (&json_ctx, i, 0);
+      do_test (&json_ctx, i, 1);
+      do_test (&json_ctx, i, -1);
+    }
+
+  for (int i = 4096; i <= 65536; i = i * 2)
+    {
+      do_test_fixed_size (&json_ctx, i, i, 0);
+      do_test_fixed_size (&json_ctx, i, i, 1);
+      do_test_fixed_size (&json_ctx, i, i, -1);
+    }
 
   json_array_end (&json_ctx);
   json_attr_object_end (&json_ctx);
