diff --git a/src/alloc-aligned.c b/src/alloc-aligned.c
index b63c5e43..e5a42357 100644
--- a/src/alloc-aligned.c
+++ b/src/alloc-aligned.c
@@ -15,17 +15,23 @@ terms of the MIT license. A copy of the license can be found in the file
 // Aligned Allocation
 // ------------------------------------------------------
 
+static inline bool mi_is_naturally_aligned( size_t size, size_t alignment ) {
+  // objects up to `MI_MEDIUM_OBJ_SIZE_MAX` are allocated aligned to their size (see `segment.c:_mi_segment_page_start`).
+  // note: the size may not be not an actual bin-size but it turns out the test below is still correct for our
+  // powers of two bin spacing (see test-api.c:test-aligned13).
+  mi_assert_internal(_mi_is_power_of_two(alignment) && (alignment > 0));
+  return (size <= MI_MEDIUM_OBJ_SIZE_MAX && alignment <= size && ((size + MI_PADDING_SIZE) & (alignment-1)) == 0);
+}
+
+
 // Fallback primitive aligned allocation -- split out for better codegen
 static mi_decl_noinline void* mi_heap_malloc_zero_aligned_at_fallback(mi_heap_t* const heap, const size_t size, const size_t alignment, const size_t offset, const bool zero) mi_attr_noexcept
 {
-  mi_assert_internal(size <= PTRDIFF_MAX);
+  mi_assert_internal(size <= (MI_MAX_ALLOC_SIZE - MI_PADDING_SIZE));
   mi_assert_internal(alignment != 0 && _mi_is_power_of_two(alignment));
 
-  const uintptr_t align_mask = alignment - 1;  // for any x, `(x & align_mask) == (x % alignment)`
-  const size_t padsize = size + MI_PADDING_SIZE;
-
-  // use regular allocation if it is guaranteed to fit the alignment constraints
-  if (offset == 0 && alignment <= padsize && padsize <= MI_MEDIUM_OBJ_SIZE_MAX && (padsize & align_mask) == 0) {
+  // use regular allocation if it is guaranteed to fit the alignment constraints.
+  if (offset == 0 && mi_is_naturally_aligned(size,alignment)) {
     void* p = _mi_heap_malloc_zero(heap, size, zero);
     mi_assert_internal(p == NULL || ((uintptr_t)p % alignment) == 0);
     return p;
@@ -57,6 +63,7 @@ static mi_decl_noinline void* mi_heap_malloc_zero_aligned_at_fallback(mi_heap_t*
   }
 
   // .. and align within the allocation
+  const uintptr_t align_mask = alignment - 1;  // for any x, `(x & align_mask) == (x % alignment)`
   const uintptr_t poffset = ((uintptr_t)p + offset) & align_mask;
   const uintptr_t adjust  = (poffset == 0 ? 0 : alignment - poffset);
   mi_assert_internal(adjust < alignment);
@@ -100,14 +107,14 @@ static void* mi_heap_malloc_zero_aligned_at(mi_heap_t* const heap, const size_t
     return NULL;
   }
 
-  if mi_unlikely(size > PTRDIFF_MAX) {          // we don't allocate more than PTRDIFF_MAX (see <https://sourceware.org/ml/libc-announce/2019/msg00001.html>)
+  if mi_unlikely(size > (MI_MAX_ALLOC_SIZE - MI_PADDING_SIZE)) { // we don't allocate more than MI_MAX_ALLOC_SIZE (see <https://sourceware.org/ml/libc-announce/2019/msg00001.html>)
     #if MI_DEBUG > 0
     _mi_error_message(EOVERFLOW, "aligned allocation request is too large (size %zu, alignment %zu)\n", size, alignment);
     #endif
     return NULL;
   }
   const uintptr_t align_mask = alignment-1;       // for any x, `(x & align_mask) == (x % alignment)`
-  const size_t padsize = size + MI_PADDING_SIZE;  // note: cannot overflow due to earlier size > PTRDIFF_MAX check
+  const size_t padsize = size + MI_PADDING_SIZE;  // note: cannot overflow due to earlier size  check
 
   // try first if there happens to be a small block available with just the right alignment
   if mi_likely(padsize <= MI_SMALL_SIZE_MAX && alignment <= padsize) {
@@ -140,15 +147,7 @@ mi_decl_nodiscard mi_decl_restrict void* mi_heap_malloc_aligned_at(mi_heap_t* he
 
 mi_decl_nodiscard mi_decl_restrict void* mi_heap_malloc_aligned(mi_heap_t* heap, size_t size, size_t alignment) mi_attr_noexcept {
   if (alignment == 0 || !_mi_is_power_of_two(alignment)) return NULL;
-  #if !MI_PADDING
-  // without padding, any small sized allocation is naturally aligned (see also `_mi_segment_page_start`)
-  if mi_likely(_mi_is_power_of_two(size) && size >= alignment && size <= MI_SMALL_SIZE_MAX)
-  #else
-  // with padding, we can only guarantee this for fixed alignments
-  if mi_likely((alignment == sizeof(void*) || (alignment == MI_MAX_ALIGN_SIZE && size > (MI_MAX_ALIGN_SIZE/2)))
-                && size <= MI_SMALL_SIZE_MAX)
-  #endif
-  {
+  if (size <= MI_SMALL_SIZE_MAX && mi_is_naturally_aligned(size,alignment)) {
     // fast path for common alignment and size
     return mi_heap_malloc_small(heap, size);
   }
diff --git a/test/test-api.c b/test/test-api.c
index 75955c49..34bfa0e6 100644
--- a/test/test-api.c
+++ b/test/test-api.c
@@ -230,6 +230,23 @@ int main(void) {
     result = (((uintptr_t)p % 0x100) == 0); // #602
     mi_free(p);
   }
+  CHECK_BODY("mimalloc-aligned13") {
+    bool ok = true;
+    for( size_t size = 1; size <= MI_SMALL_SIZE_MAX && ok; size++ ) {
+      for(size_t align = 1; align <= size && ok; align *= 2 ) {
+        void* p = mi_malloc_aligned(size,align);
+        ok = (p != NULL && ((uintptr_t)p % align) == 0);
+        mi_free(p);       
+        /*
+        if (ok && align <= size && ((size + MI_PADDING_SIZE) & (align-1)) == 0) {
+          size_t bsize = mi_good_size(size);
+          ok = (align <= bsize && ((bsize + MI_PADDING_SIZE) & (align-1)) == 0);
+        }
+        */
+      }
+    }
+    result = ok;
+  }
   CHECK_BODY("malloc-aligned-at1") {
     void* p = mi_malloc_aligned_at(48,32,0); result = (p != NULL && ((uintptr_t)(p) + 0) % 32 == 0); mi_free(p);
   };