diff --git a/libImaging/Storage.c b/libImaging/Storage.c
index 096717ce3..f40840671 100644
--- a/libImaging/Storage.c
+++ b/libImaging/Storage.c
@@ -345,27 +345,30 @@ ImagingNewBlock(const char *mode, int xsize, int ysize)
 {
     Imaging im;
     Py_ssize_t y, i;
-    Py_ssize_t bytes;
 
     im = ImagingNewPrologue(mode, xsize, ysize);
     if (!im)
         return NULL;
 
-
+    /* We shouldn't overflow, since the threshold defined
+       below says that we're only going to allocate max 4M
+       here before going to the array allocator. Check anyway.
+    */
     if (im->linesize &&
-        im->ysize > SIZE_MAX / im->linesize) {
+        im->ysize > INT_MAX / im->linesize) {
         /* punt if we're going to overflow */
         return NULL;
     }
-    /* Use a single block */        
-    bytes = ((Py_ssize_t) im->ysize) * im->linesize;
-    if (bytes <= 0)
+
+    if (im->ysize * im->linesize <= 0) {
         /* some platforms return NULL for malloc(0); this fix
            prevents MemoryError on zero-sized images on such
            platforms */
-        bytes = 1;
-    /* malloc check ok, overflow check above */
-    im->block = (char *) calloc(bytes, 1);
+        im->block = (char *) malloc(1);
+    } else {
+        /* malloc check ok, overflow check above */
+        im->block = (char *) calloc(im->ysize, im->linesize);
+    }
 
     if (im->block) {
         for (y = i = 0; y < im->ysize; y++) {