diff --git a/malloc/malloc.c b/malloc/malloc.c
index 20874a5dfe..a49e211925 100644
--- a/malloc/malloc.c
+++ b/malloc/malloc.c
@@ -4703,14 +4703,17 @@ _int_memalign (mstate av, size_t alignment, size_t bytes)
 {
   mchunkptr p, newp;
 
-  if (bytes > PTRDIFF_MAX)
+  if (bytes > PTRDIFF_MAX || alignment > PTRDIFF_MAX)
     {
       __set_errno (ENOMEM);
       return NULL;
     }
   size_t nb = checked_request2size (bytes);
 
-  /* Call malloc with worst case padding to hit alignment.  */
+  /* Call malloc with worst case padding to hit alignment.  ALIGNMENT is a
+     power of 2, so it tops out at (PTRDIFF_MAX >> 1) + 1, leaving plenty of
+     space to add MINSIZE and whatever checked_request2size adds to BYTES to
+     get NB.  Consequently, total below also does not overflow.  */
   void *m = _int_malloc (av, nb + alignment + MINSIZE);
 
   if (m == NULL)
diff --git a/malloc/tst-malloc-too-large.c b/malloc/tst-malloc-too-large.c
index 34847067dc..ee231285bf 100644
--- a/malloc/tst-malloc-too-large.c
+++ b/malloc/tst-malloc-too-large.c
@@ -152,7 +152,6 @@ test_large_allocations (size_t size)
 }
 
 
-static long pagesize;
 
 /* This function tests the following aligned memory allocation functions
    using several valid alignments and precedes each allocation test with a
@@ -171,8 +170,8 @@ test_large_aligned_allocations (size_t size)
 
   /* All aligned memory allocation functions expect an alignment that is a
      power of 2.  Given this, we test each of them with every valid
-     alignment from 1 thru PAGESIZE.  */
-  for (align = 1; align <= pagesize; align *= 2)
+     alignment for the type of ALIGN, i.e. until it wraps to 0.  */
+  for (align = 1; align > 0; align <<= 1)
     {
       test_setup ();
 #if __GNUC_PREREQ (7, 0)
@@ -265,11 +264,6 @@ do_test (void)
   DIAG_IGNORE_NEEDS_COMMENT (7, "-Walloc-size-larger-than=");
 #endif
 
-  /* Aligned memory allocation functions need to be tested up to alignment
-     size equivalent to page size, which should be a power of 2.  */
-  pagesize = sysconf (_SC_PAGESIZE);
-  TEST_VERIFY_EXIT (powerof2 (pagesize));
-
   /* Loop 1: Ensure that all allocations with SIZE close to SIZE_MAX, i.e.
      in the range (SIZE_MAX - 2^14, SIZE_MAX], fail.