diff -r 26f6d8cc2749 Modules/selectmodule.c
--- a/Modules/selectmodule.c	Thu Jan 28 15:44:10 2016 +0100
+++ b/Modules/selectmodule.c	Thu Jan 28 16:09:10 2016 +0100
@@ -1490,7 +1490,8 @@ pyepoll_poll(pyEpoll_Object *self, PyObj
     int maxevents = -1;
     int nfds, i;
     PyObject *elist = NULL, *etuple = NULL;
-    struct epoll_event *evs = NULL;
+    struct epoll_event evs_nomalloc[FD_SETSIZE-1];
+    struct epoll_event *evs = evs_nomalloc;
     _PyTime_t timeout, ms, deadline;
 
     if (self->epfd < 0)
@@ -1530,17 +1531,19 @@ pyepoll_poll(pyEpoll_Object *self, PyObj
     if (maxevents == -1) {
         maxevents = FD_SETSIZE-1;
     }
-    else if (maxevents < 1) {
+    else if (maxevents == 0) {
         PyErr_Format(PyExc_ValueError,
                      "maxevents must be greater than 0, got %d",
                      maxevents);
         return NULL;
     }
 
-    evs = PyMem_New(struct epoll_event, maxevents);
-    if (evs == NULL) {
-        PyErr_NoMemory();
-        return NULL;
+    if (maxevents >= FD_SETSIZE) {
+	evs = PyMem_New(struct epoll_event, maxevents);
+	if (evs == NULL) {
+	    PyErr_NoMemory();
+	    return NULL;
+	}
     }
 
     do {
@@ -1587,7 +1590,9 @@ pyepoll_poll(pyEpoll_Object *self, PyObj
     }
 
     error:
-    PyMem_Free(evs);
+    if (evs != evs_nomalloc) {
+	PyMem_Free(evs);
+    }
     return elist;
 }