diff --git a/src/allocator.c b/src/allocator.c
index e6ea77217..861678973 100644
--- a/src/allocator.c
+++ b/src/allocator.c
@@ -601,10 +601,7 @@ _dispatch_alloc_init(void)
 	// Double-check our math. These are all compile time checks and don't
 	// generate code.
 
-	dispatch_assert(sizeof(bitmap_t) == BYTES_PER_BITMAP);
 	dispatch_assert(sizeof(bitmap_t) == BYTES_PER_SUPERMAP);
-	dispatch_assert(sizeof(struct dispatch_magazine_header_s) ==
-			SIZEOF_HEADER);
 
 	dispatch_assert(sizeof(struct dispatch_continuation_s) <=
 			DISPATCH_CONTINUATION_SIZE);
@@ -614,8 +611,6 @@ _dispatch_alloc_init(void)
 	dispatch_assert(sizeof(struct dispatch_magazine_s) == BYTES_PER_MAGAZINE);
 
 	// The header and maps sizes should match what we computed.
-	dispatch_assert(SIZEOF_HEADER ==
-			sizeof(((struct dispatch_magazine_s *)0x0)->header));
 	dispatch_assert(SIZEOF_MAPS ==
 			sizeof(((struct dispatch_magazine_s *)0x0)->maps));
 
diff --git a/src/allocator_internal.h b/src/allocator_internal.h
index abe4a1d43..fc34b955f 100644
--- a/src/allocator_internal.h
+++ b/src/allocator_internal.h
@@ -97,25 +97,21 @@
 // Use the largest type your platform is comfortable doing atomic ops with.
 // TODO: rdar://11477843
 typedef unsigned long bitmap_t;
-#if defined(__LP64__)
-#define BYTES_PER_BITMAP 8
-#else
-#define BYTES_PER_BITMAP 4
-#endif
+#define BYTES_PER_BITMAP sizeof(bitmap_t)
 
 #define BITMAP_C(v) ((bitmap_t)(v))
 #define BITMAP_ALL_ONES (~BITMAP_C(0))
 
 // Stop configuring.
 
-#define CONTINUATIONS_PER_BITMAP (BYTES_PER_BITMAP * 8)
-#define BITMAPS_PER_SUPERMAP (BYTES_PER_SUPERMAP * 8)
+#define CONTINUATIONS_PER_BITMAP (BYTES_PER_BITMAP * CHAR_BIT)
+#define BITMAPS_PER_SUPERMAP (BYTES_PER_SUPERMAP * CHAR_BIT)
 
 #define BYTES_PER_MAGAZINE (PAGES_PER_MAGAZINE * DISPATCH_ALLOCATOR_PAGE_SIZE)
 #define CONSUMED_BYTES_PER_BITMAP (BYTES_PER_BITMAP + \
 		(DISPATCH_CONTINUATION_SIZE * CONTINUATIONS_PER_BITMAP))
 
-#define BYTES_PER_SUPERMAP BYTES_PER_BITMAP
+#define BYTES_PER_SUPERMAP sizeof(bitmap_t)
 #define CONSUMED_BYTES_PER_SUPERMAP (BYTES_PER_SUPERMAP + \
 		(BITMAPS_PER_SUPERMAP * CONSUMED_BYTES_PER_BITMAP))
 
@@ -147,11 +143,7 @@ typedef unsigned long bitmap_t;
 
 #define PADDING_TO_CONTINUATION_SIZE(x) (ROUND_UP_TO_CONTINUATION_SIZE(x) - (x))
 
-#if defined(__LP64__)
-#define SIZEOF_HEADER 16
-#else
-#define SIZEOF_HEADER 8
-#endif
+#define SIZEOF_HEADER (sizeof(struct dispatch_magazine_header_s))
 
 #define SIZEOF_SUPERMAPS (BYTES_PER_SUPERMAP * SUPERMAPS_PER_MAGAZINE)
 #define SIZEOF_MAPS (BYTES_PER_BITMAP * BITMAPS_PER_SUPERMAP * \