diff --git a/Include/pymem.h b/Include/pymem.h
index 0ab9463..caa58b1 100644
--- a/Include/pymem.h
+++ b/Include/pymem.h
@@ -67,8 +67,12 @@
    for malloc(0), which would be treated as an error. Some platforms
    would return a pointer with no memory behind it, which would break
    pymalloc. To solve these problems, allocate an extra byte. */
-#define PyMem_MALLOC(n)         malloc((n) ? (n) : 1)
-#define PyMem_REALLOC(p, n)     realloc((p), (n) ? (n) : 1)
+/* Returns NULL to indicate error if a negative size or size larger than
+   Py_ssize_t can represent is supplied.  Helps prevents security holes. */
+#define PyMem_MALLOC(n)		(((n) < 0 || (n) > PY_SSIZE_T_MAX) ? NULL \
+				: malloc((n) ? (n) : 1))
+#define PyMem_REALLOC(p, n)	(((n) < 0 || (n) > PY_SSIZE_T_MAX) ? NULL \
+				: realloc((p), (n) ? (n) : 1))
 #define PyMem_FREE		free
 
 #endif	/* PYMALLOC_DEBUG */
@@ -77,24 +81,31 @@
  * Type-oriented memory interface
  * ==============================
  *
- * These are carried along for historical reasons.  There's rarely a good
- * reason to use them anymore (you can just as easily do the multiply and
- * cast yourself).
+ * Allocate memory for n objects of the given type.  Returns a new pointer
+ * or NULL if the request was too large or memory allocation failed.  Use
+ * these macros rather than doing the multiplication yourself so that proper
+ * overflow checking is always done.
  */
 
 #define PyMem_New(type, n) \
-  ( assert((n) <= PY_SIZE_MAX / sizeof(type)) , \
+  ( ((n) > PY_SSIZE_T_MAX / sizeof(type)) ? NULL : \
 	( (type *) PyMem_Malloc((n) * sizeof(type)) ) )
 #define PyMem_NEW(type, n) \
-  ( assert((n) <= PY_SIZE_MAX / sizeof(type)) , \
+  ( ((n) > PY_SSIZE_T_MAX / sizeof(type)) ? NULL : \
 	( (type *) PyMem_MALLOC((n) * sizeof(type)) ) )
 
+/*
+ * The value of (p) is always clobbered by this macro regardless of success.
+ * The caller MUST check if (p) is NULL afterwards and deal with the memory
+ * error if so.  This means the original value of (p) MUST be saved for the
+ * caller's memory error handler to not lose track of it.
+ */
 #define PyMem_Resize(p, type, n) \
-  ( assert((n) <= PY_SIZE_MAX / sizeof(type)) , \
-	( (p) = (type *) PyMem_Realloc((p), (n) * sizeof(type)) ) )
+  ( (p) = ((n) > PY_SSIZE_T_MAX / sizeof(type)) ? NULL : \
+	(type *) PyMem_Realloc((p), (n) * sizeof(type)) )
 #define PyMem_RESIZE(p, type, n) \
-  ( assert((n) <= PY_SIZE_MAX / sizeof(type)) , \
-	( (p) = (type *) PyMem_REALLOC((p), (n) * sizeof(type)) ) )
+  ( (p) = ((n) > PY_SSIZE_T_MAX / sizeof(type)) ? NULL : \
+	(type *) PyMem_REALLOC((p), (n) * sizeof(type)) )
 
 /* PyMem{Del,DEL} are left over from ancient days, and shouldn't be used
  * anymore.  They're just confusing aliases for PyMem_{Free,FREE} now.
diff --git a/Misc/NEWS b/Misc/NEWS
index 0f36f17..222e408 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -12,6 +12,13 @@
 Core and builtins
 -----------------
 
+- Issue #2620: Overflow checking when allocating or reallocating memory
+  was not always being done properly in some python types and extension
+  modules.  PyMem_MALLOC, PyMem_REALLOC, PyMem_NEW and PyMem_RESIZE have
+  all been updated to perform better checks and places in the code that
+  would previously leak memory on the error path when such an allocation
+  failed have been fixed.
+
 - Issue #2242: Fix a crash when decoding invalid utf-7 input on certain
   Windows / Visual Studio versions.
 
diff --git a/Modules/almodule.c b/Modules/almodule.c
index 0a45d2e..e4481cd 100644
--- a/Modules/almodule.c
+++ b/Modules/almodule.c
@@ -1633,9 +1633,11 @@
 	if (nvals < 0)
 		goto cleanup;
 	if (nvals > setsize) {
+		ALvalue *old_return_set = return_set;
 		setsize = nvals;
 		PyMem_RESIZE(return_set, ALvalue, setsize);
 		if (return_set == NULL) {
+			return_set = old_return_set;
 			PyErr_NoMemory();
 			goto cleanup;
 		}
diff --git a/Modules/arraymodule.c b/Modules/arraymodule.c
index eafea98..f262d20 100644
--- a/Modules/arraymodule.c
+++ b/Modules/arraymodule.c
@@ -816,6 +816,7 @@
 array_do_extend(arrayobject *self, PyObject *bb)
 {
 	Py_ssize_t size;
+	char *old_item;
 
 	if (!array_Check(bb))
 		return array_iter_extend(self, bb);
@@ -831,10 +832,11 @@
 			return -1;
 	}
 	size = self->ob_size + b->ob_size;
+	old_item = self->ob_item;
         PyMem_RESIZE(self->ob_item, char, size*self->ob_descr->itemsize);
         if (self->ob_item == NULL) {
-                PyObject_Del(self);
-                PyErr_NoMemory();
+		self->ob_item = old_item;
+		PyErr_NoMemory();
 		return -1;
         }
 	memcpy(self->ob_item + self->ob_size*self->ob_descr->itemsize,
@@ -886,7 +888,7 @@
 			if (size > PY_SSIZE_T_MAX / n) {
 				return PyErr_NoMemory();
 			}
-			PyMem_Resize(items, char, n * size);
+			PyMem_RESIZE(items, char, n * size);
 			if (items == NULL)
 				return PyErr_NoMemory();
 			p = items;
diff --git a/Modules/selectmodule.c b/Modules/selectmodule.c
index 9eaae84..4deab6f 100644
--- a/Modules/selectmodule.c
+++ b/Modules/selectmodule.c
@@ -349,10 +349,12 @@
 {
 	Py_ssize_t i, pos;
 	PyObject *key, *value;
+        struct pollfd *old_ufds = self->ufds;
 
 	self->ufd_len = PyDict_Size(self->dict);
-	PyMem_Resize(self->ufds, struct pollfd, self->ufd_len);
+	PyMem_RESIZE(self->ufds, struct pollfd, self->ufd_len);
 	if (self->ufds == NULL) {
+                self->ufds = old_ufds;
 		PyErr_NoMemory();
 		return 0;
 	}
diff --git a/Objects/obmalloc.c b/Objects/obmalloc.c
index 03add6b..2d77906 100644
--- a/Objects/obmalloc.c
+++ b/Objects/obmalloc.c
@@ -727,6 +727,15 @@
 	uint size;
 
 	/*
+	 * Limit ourselves to PY_SSIZE_T_MAX bytes to prevent security holes.
+	 * Most python internals blindly use a signed Py_ssize_t to track
+	 * things without checking for overflows or negatives.
+	 * As size_t is unsigned, checking for nbytes < 0 is not required.
+	 */
+	if (nbytes > PY_SSIZE_T_MAX)
+		return NULL;
+
+	/*
 	 * This implicitly redirects malloc(0).
 	 */
 	if ((nbytes - 1) < SMALL_REQUEST_THRESHOLD) {
@@ -1130,6 +1139,15 @@
 	if (p == NULL)
 		return PyObject_Malloc(nbytes);
 
+	/*
+	 * Limit ourselves to PY_SSIZE_T_MAX bytes to prevent security holes.
+	 * Most python internals blindly use a signed Py_ssize_t to track
+	 * things without checking for overflows or negatives.
+	 * As size_t is unsigned, checking for nbytes < 0 is not required.
+	 */
+	if (nbytes > PY_SSIZE_T_MAX)
+		return NULL;
+
 	pool = POOL_ADDR(p);
 	if (Py_ADDRESS_IN_RANGE(p, pool)) {
 		/* We're in charge of this block */