diff --git a/Modules/_bz2module.c b/Modules/_bz2module.c
index 3890b60b1b8..f0d9588fe55 100644
--- a/Modules/_bz2module.c
+++ b/Modules/_bz2module.c
@@ -277,11 +277,11 @@ BZ2_Malloc(void* ctx, int items, int size)
 {
     if (items < 0 || size < 0)
         return NULL;
-    if ((size_t)items > (size_t)PY_SSIZE_T_MAX / (size_t)size)
+    if (size != 0 && (size_t)items > (size_t)PY_SSIZE_T_MAX / (size_t)size)
         return NULL;
     /* PyMem_Malloc() cannot be used: compress() and decompress()
        release the GIL */
-    return PyMem_RawMalloc(items * size);
+    return PyMem_RawMalloc((size_t)items * (size_t)size);
 }
 
 static void
diff --git a/Modules/_lzmamodule.c b/Modules/_lzmamodule.c
index 7b501d8202d..bb7a7ec50ce 100644
--- a/Modules/_lzmamodule.c
+++ b/Modules/_lzmamodule.c
@@ -108,7 +108,7 @@ catch_lzma_error(lzma_ret lzret)
 static void*
 PyLzma_Malloc(void *opaque, size_t items, size_t size)
 {
-    if (items > (size_t)PY_SSIZE_T_MAX / size)
+    if (size != 0 && items > (size_t)PY_SSIZE_T_MAX / size)
         return NULL;
     /* PyMem_Malloc() cannot be used:
        the GIL is not held when lzma_code() is called */
diff --git a/Modules/zlibmodule.c b/Modules/zlibmodule.c
index 36a3835e421..00bbe21fc0b 100644
--- a/Modules/zlibmodule.c
+++ b/Modules/zlibmodule.c
@@ -117,11 +117,11 @@ newcompobject(PyTypeObject *type)
 static void*
 PyZlib_Malloc(voidpf ctx, uInt items, uInt size)
 {
-    if (items > (size_t)PY_SSIZE_T_MAX / size)
+    if (size != 0 && items > (size_t)PY_SSIZE_T_MAX / size)
         return NULL;
     /* PyMem_Malloc() cannot be used: the GIL is not held when
        inflate() and deflate() are called */
-    return PyMem_RawMalloc(items * size);
+    return PyMem_RawMalloc((size_t)items * (size_t)size);
 }
 
 static void