diff --git a/include/mimalloc-internal.h b/include/mimalloc-internal.h
index 40bb1349..243a45a9 100644
--- a/include/mimalloc-internal.h
+++ b/include/mimalloc-internal.h
@@ -481,11 +481,11 @@ static inline mi_slice_t* mi_slice_first(const mi_slice_t* slice) {
 
 // Get the page containing the pointer
 static inline mi_page_t* _mi_segment_page_of(const mi_segment_t* segment, const void* p) {
+  mi_assert_internal(p > segment);
   ptrdiff_t diff = (uint8_t*)p - (uint8_t*)segment;
-  mi_assert_internal(diff >= 0 && diff <= (ptrdiff_t)MI_SEGMENT_SIZE /* can be equal for large alignment */);
-  if (diff == MI_SEGMENT_SIZE) diff--;
+  mi_assert_internal(diff > 0 && diff <= (ptrdiff_t)MI_SEGMENT_SIZE);
   size_t idx = (size_t)diff >> MI_SEGMENT_SLICE_SHIFT;
-  mi_assert_internal(idx < segment->slice_entries);
+  mi_assert_internal(idx <= segment->slice_entries);
   mi_slice_t* slice0 = (mi_slice_t*)&segment->slices[idx];
   mi_slice_t* slice = mi_slice_first(slice0);  // adjust to the block that holds the page data
   mi_assert_internal(slice->slice_offset == 0);
diff --git a/include/mimalloc-types.h b/include/mimalloc-types.h
index b5931789..b960a460 100644
--- a/include/mimalloc-types.h
+++ b/include/mimalloc-types.h
@@ -381,7 +381,7 @@ typedef struct mi_segment_s {
   mi_segment_kind_t kind;
   _Atomic(mi_threadid_t) thread_id;      // unique id of the thread owning this segment
   size_t            slice_entries;       // entries in the `slices` array, at most `MI_SLICES_PER_SEGMENT`
-  mi_slice_t        slices[MI_SLICES_PER_SEGMENT];
+  mi_slice_t        slices[MI_SLICES_PER_SEGMENT+1];  // one more for huge blocks with large alignment
 } mi_segment_t;
 
 
diff --git a/src/alloc-aligned.c b/src/alloc-aligned.c
index 76ed0ed7..06ed5272 100644
--- a/src/alloc-aligned.c
+++ b/src/alloc-aligned.c
@@ -63,7 +63,7 @@ static mi_decl_noinline void* mi_heap_malloc_zero_aligned_at_fallback(mi_heap_t*
   void* aligned_p = (adjust == alignment ? p : (void*)((uintptr_t)p + adjust));
   if (aligned_p != p) { mi_page_set_has_aligned(_mi_ptr_page(p), true);  }
     
-  mi_assert_internal(p == _mi_page_ptr_unalign(_mi_ptr_segment(aligned_p), _mi_ptr_page(aligned_p), aligned_p));
+  // mi_assert_internal(p == _mi_page_ptr_unalign(_mi_ptr_segment(aligned_p), _mi_ptr_page(aligned_p), aligned_p));
   mi_assert_internal(((uintptr_t)aligned_p + offset) % alignment == 0);
   
   #if MI_TRACK_ENABLED
diff --git a/src/segment.c b/src/segment.c
index c743f02f..f637e7a9 100644
--- a/src/segment.c
+++ b/src/segment.c
@@ -277,7 +277,7 @@ static bool mi_segment_is_valid(mi_segment_t* segment, mi_segments_tld_t* tld) {
       }
       // and the last entry as well (for coalescing)
       const mi_slice_t* last = slice + slice->slice_count - 1;
-      if (last > slice && last < mi_segment_slices_end(segment)) {
+      if (last > slice && last <= mi_segment_slices_end(segment)) {
         mi_assert_internal(last->slice_offset == (slice->slice_count-1)*sizeof(mi_slice_t));
         mi_assert_internal(last->slice_count == 0);
         mi_assert_internal(last->xblock_size == 1);
@@ -709,9 +709,13 @@ static mi_page_t* mi_segment_span_allocate(mi_segment_t* segment, size_t slice_i
 
   // and also for the last one (if not set already) (the last one is needed for coalescing)
   // note: the cast is needed for ubsan since the index can be larger than MI_SLICES_PER_SEGMENT for huge allocations (see #543)
-  mi_slice_t* last = &((mi_slice_t*)segment->slices)[slice_index + slice_count - 1]; 
-  if (last < mi_segment_slices_end(segment) && last >= slice) {
-    last->slice_offset = (uint32_t)(sizeof(mi_slice_t)*(slice_count-1));
+  size_t slice_last_index = slice_index + slice_count - 1;
+  if (slice_last_index >= segment->slice_entries) { 
+    slice_last_index = segment->slice_entries; 
+  }
+  mi_slice_t* last = &((mi_slice_t*)segment->slices)[slice_last_index]; 
+  if (last <= mi_segment_slices_end(segment) && last >= slice) {
+    last->slice_offset = (uint32_t)(sizeof(mi_slice_t)*(slice_last_index - slice_index));
     last->slice_count = 0;
     last->xblock_size = 1;
   }
@@ -853,7 +857,7 @@ static mi_segment_t* mi_segment_init(mi_segment_t* segment, size_t required, siz
   if (!is_zero) {
     ptrdiff_t ofs = offsetof(mi_segment_t, next);
     size_t    prefix = offsetof(mi_segment_t, slices) - ofs;
-    memset((uint8_t*)segment+ofs, 0, prefix + sizeof(mi_slice_t)*segment_slices);
+    memset((uint8_t*)segment+ofs, 0, prefix + sizeof(mi_slice_t)*(segment_slices+1));  // one more
   }
 
   if (!commit_info_still_good) {