diff --git a/Include/pymem.h b/Include/pymem.h
index 86a69e4..d09f38c 100644
--- a/Include/pymem.h
+++ b/Include/pymem.h
@@ -111,13 +111,18 @@
 /* Macros */
 #define PyMem_NEW(type, n) \
 	( (type *) PyMem_MALLOC(_PyMem_EXTRA + (n) * sizeof(type)) )
-#define PyMem_RESIZE(p, type, n) \
-	if ((p) == NULL) \
-		(p) = (type *)(PyMem_MALLOC( \
-				    _PyMem_EXTRA + (n) * sizeof(type))); \
-	else \
-		(p) = (type *)(PyMem_REALLOC((p), \
-				    _PyMem_EXTRA + (n) * sizeof(type)))
+
+/* See comment near MALLOC_ZERO_RETURNS_NULL in pyport.h. */
+#define PyMem_RESIZE(p, type, n)			\
+	do {						\
+		size_t _sum = (n) * sizeof(type);	\
+		if (!_sum)				\
+			_sum = 1;			\
+		(p) = (type *)((p) ?			\
+			       PyMem_REALLOC(p, _sum) :	\
+			       PyMem_MALLOC(_sum));	\
+	} while (0)
+
 #define PyMem_DEL(p) PyMem_FREE(p)
 
 /* PyMem_XDEL is deprecated. To avoid the call when p is NULL,
diff --git a/Include/pyport.h b/Include/pyport.h
index 271ec43..a831b26 100644
--- a/Include/pyport.h
+++ b/Include/pyport.h
@@ -366,8 +366,16 @@
 #endif
 
 #ifdef MALLOC_ZERO_RETURNS_NULL
-/* XXX Always allocate one extra byte, since some malloc's return NULL
-   XXX for malloc(0) or realloc(p, 0). */
+/* Allocate an extra byte if the platform malloc(0) returns NULL.
+   Caution:  this bears no relation to whether realloc(p, 0) returns NULL
+   when p != NULL.  Even on platforms where malloc(0) does not return NULL,
+   realloc(p, 0) may act like free(p) and return NULL.  Examples include
+   Windows, and Python's own obmalloc.c (as of 2-Mar-2002).  For whatever
+   reason, our docs promise that PyMem_Realloc(p, 0) won't act like
+   free(p) or return NULL, so realloc() calls may have to be hacked
+   too, but MALLOC_ZERO_RETURNS_NULL's state is irrelevant to realloc (it
+   needs a different hack).
+*/
 #define _PyMem_EXTRA 1
 #else
 #define _PyMem_EXTRA 0
diff --git a/Objects/object.c b/Objects/object.c
index 8babf79..bcc129c 100644
--- a/Objects/object.c
+++ b/Objects/object.c
@@ -1894,11 +1894,8 @@
 void *
 PyMem_Realloc(void *p, size_t nbytes)
 {
-#if _PyMem_EXTRA > 0
-	if (nbytes == 0)
-		nbytes = _PyMem_EXTRA;
-#endif
-	return PyMem_REALLOC(p, nbytes);
+	/* See comment near MALLOC_ZERO_RETURNS_NULL in pyport.h. */
+	return PyMem_REALLOC(p, nbytes ? nbytes : 1);
 }
 
 void