diff --git a/driver/others/memory.c b/driver/others/memory.c
index 8e24773841..eea073259e 100644
--- a/driver/others/memory.c
+++ b/driver/others/memory.c
@@ -2825,18 +2825,19 @@ void *blas_memory_alloc(int procpos){
 
   position = 0;
 
-#if (defined(SMP) || defined(USE_LOCKING)) && !defined(USE_OPENMP)
-  LOCK_COMMAND(&alloc_lock);
-#endif
+  /* Slots of memory[] are claimed with their own lock rather than alloc_lock,
+     so that threads of the application calling OpenBLAS concurrently (e.g.
+     from an OpenMP parallel region) don't all take the same mutex twice per
+     call. */
   do {
     RMB;
-#if defined(USE_OPENMP)
+#if defined(SMP) || defined(USE_LOCKING)
     if (!memory[position].used) {
       blas_lock((BLASULONG *)&memory[position].lock);
 #endif
       if (!memory[position].used) goto allocation;
 
-#if defined(USE_OPENMP)
+#if defined(SMP) || defined(USE_LOCKING)
       blas_unlock((BLASULONG *)&memory[position].lock);
     }
 #endif
@@ -2844,6 +2845,9 @@ void *blas_memory_alloc(int procpos){
 
   } while (position < NUM_BUFFERS);
 
+#if (defined(SMP) || defined(USE_LOCKING)) && !defined(USE_OPENMP)
+  LOCK_COMMAND(&alloc_lock);
+#endif
   if (memory_overflowed) {
 
     do {
@@ -2874,9 +2878,7 @@ void *blas_memory_alloc(int procpos){
 #endif
 
   memory[position].used = 1;
-#if (defined(SMP) || defined(USE_LOCKING)) && !defined(USE_OPENMP)
-  UNLOCK_COMMAND(&alloc_lock);
-#else
+#if defined(SMP) || defined(USE_LOCKING)
   blas_unlock((BLASULONG *)&memory[position].lock);
 #endif
   if (!memory[position].addr) {
@@ -2946,13 +2948,7 @@ void *blas_memory_alloc(int procpos){
 
     } while ((BLASLONG)map_address == -1);
 
-#if (defined(SMP) || defined(USE_LOCKING)) && !defined(USE_OPENMP)
-    LOCK_COMMAND(&alloc_lock);
-#endif
     memory[position].addr = map_address;
-#if (defined(SMP) || defined(USE_LOCKING)) && !defined(USE_OPENMP)
-    UNLOCK_COMMAND(&alloc_lock);
-#endif
 
 #ifdef DEBUG
     printf("  Mapping Succeeded. %p(%d)\n", (void *)memory[position].addr, position);
@@ -3127,48 +3123,46 @@ void blas_memory_free(void *free_area){
 #endif
 
   position = 0;
-#if (defined(SMP) || defined(USE_LOCKING)) && !defined(USE_OPENMP)
-  LOCK_COMMAND(&alloc_lock);
-#endif
+  /* Only the thread holding a buffer of memory[] frees it, so its slot is
+     released without alloc_lock, as it is claimed in blas_memory_alloc. */
   while ((position < NUM_BUFFERS) && (memory[position].addr != free_area))
     position++;
 
-  if (position >= NUM_BUFFERS && !memory_overflowed) goto error;
+  if (likely(position < NUM_BUFFERS)) {
+#ifdef DEBUG
+    printf("  Position : %d\n", position);
+#endif
+    // arm: ensure all writes are finished before other thread takes this memory
+    WMB;
+
+    memory[position].used = 0;
 
 #ifdef DEBUG
-  if (memory[position].addr != free_area) goto error;
-  printf("  Position : %d\n", position);
+    printf("Unmap Succeeded.\n\n");
 #endif
-  if (unlikely(memory_overflowed && position >= NUM_BUFFERS)) {
-    while ((position < NUM_BUFFERS+NEW_BUFFERS) && (newmemory[position-NUM_BUFFERS].addr != free_area))
-      position++;
-  // arm: ensure all writes are finished before other thread takes this memory
-  WMB;
-if (position - NUM_BUFFERS >= NEW_BUFFERS) goto error;
-  newmemory[position-NUM_BUFFERS].used = 0;
+    return;
+  }
+
 #if (defined(SMP) || defined(USE_LOCKING)) && !defined(USE_OPENMP)
-  UNLOCK_COMMAND(&alloc_lock);
+  LOCK_COMMAND(&alloc_lock);
 #endif
+  if (!memory_overflowed) goto error;
 
-#ifdef DEBUG
-  printf("Unmap from overflow area succeeded.\n\n");
-#endif
-  return;
-} else {
+  while ((position < NUM_BUFFERS+NEW_BUFFERS) && (newmemory[position-NUM_BUFFERS].addr != free_area))
+    position++;
   // arm: ensure all writes are finished before other thread takes this memory
   WMB;
-
-  memory[position].used = 0;
+  if (position - NUM_BUFFERS >= NEW_BUFFERS) goto error;
+  newmemory[position-NUM_BUFFERS].used = 0;
 #if (defined(SMP) || defined(USE_LOCKING)) && !defined(USE_OPENMP)
   UNLOCK_COMMAND(&alloc_lock);
 #endif
 
 #ifdef DEBUG
-  printf("Unmap Succeeded.\n\n");
+  printf("Unmap from overflow area succeeded.\n\n");
 #endif
-
   return;
-}
+
  error:
   printf("BLAS : Bad memory unallocation! : %4d  %p\n", position,  free_area);