diff --git a/Modules/selectmodule.c b/Modules/selectmodule.c
index d234d504cb5167..327a079b5e97a3 100644
--- a/Modules/selectmodule.c
+++ b/Modules/selectmodule.c
@@ -790,12 +790,16 @@ poll_dealloc(PyObject *op)
 #ifdef HAVE_SYS_DEVPOLL_H
 static PyMethodDef devpoll_methods[];
 
+#define DEVPOLL_IN_BUFFER_SIZE 128
+#define DEVPOLL_MAX_OUT_BUFFER_SIZE 1024
+
 typedef struct {
     PyObject_HEAD
     int fd_devpoll;
-    int max_n_fds;
     int n_fds;
+    int out_size;
     struct pollfd *fds;
+    struct pollfd *out_fds;
 } devpollObject;
 
 #define devpollObject_CAST(op)  ((devpollObject *)(op))
@@ -848,7 +852,7 @@ internal_devpoll_register(devpollObject *self, int fd,
         self->fds[self->n_fds].fd = fd;
         self->fds[self->n_fds].events = POLLREMOVE;
 
-        if (++self->n_fds == self->max_n_fds) {
+        if (++self->n_fds == DEVPOLL_IN_BUFFER_SIZE) {
             if (devpoll_flush(self))
                 return NULL;
         }
@@ -857,7 +861,7 @@ internal_devpoll_register(devpollObject *self, int fd,
     self->fds[self->n_fds].fd = fd;
     self->fds[self->n_fds].events = (signed short)events;
 
-    if (++self->n_fds == self->max_n_fds) {
+    if (++self->n_fds == DEVPOLL_IN_BUFFER_SIZE) {
         if (devpoll_flush(self))
             return NULL;
     }
@@ -929,7 +933,7 @@ select_devpoll_unregister_impl(devpollObject *self, int fd)
     self->fds[self->n_fds].fd = fd;
     self->fds[self->n_fds].events = POLLREMOVE;
 
-    if (++self->n_fds == self->max_n_fds) {
+    if (++self->n_fds == DEVPOLL_IN_BUFFER_SIZE) {
         if (devpoll_flush(self))
             return NULL;
     }
@@ -989,8 +993,8 @@ select_devpoll_poll_impl(devpollObject *self, PyObject *timeout_obj)
     if (devpoll_flush(self))
         return NULL;
 
-    dvp.dp_fds = self->fds;
-    dvp.dp_nfds = self->max_n_fds;
+    dvp.dp_fds = self->out_fds;
+    dvp.dp_nfds = self->out_size;
     dvp.dp_timeout = (int)ms;
 
     if (timeout >= 0) {
@@ -1034,8 +1038,8 @@ select_devpoll_poll_impl(devpollObject *self, PyObject *timeout_obj)
         return NULL;
 
     for (i = 0; i < poll_result; i++) {
-        num1 = PyLong_FromLong(self->fds[i].fd);
-        num2 = PyLong_FromLong(self->fds[i].revents);
+        num1 = PyLong_FromLong(self->out_fds[i].fd);
+        num2 = PyLong_FromLong(self->out_fds[i].revents);
         if ((num1 == NULL) || (num2 == NULL)) {
             Py_XDECREF(num1);
             Py_XDECREF(num2);
@@ -1128,12 +1132,12 @@ static devpollObject *
 newDevPollObject(PyObject *module)
 {
     devpollObject *self;
-    int fd_devpoll, limit_result;
-    struct pollfd *fds;
+    int fd_devpoll, limit_result, out_size;
+    struct pollfd *fds, *out_fds;
     struct rlimit limit;
 
     /*
-    ** If we try to process more that getrlimit()
+    ** If we try to process more than getrlimit()
     ** fds, the kernel will give an error, so
     ** we set the limit here. It is a dynamic
     ** value, because we can change rlimit() anytime.
@@ -1144,27 +1148,46 @@ newDevPollObject(PyObject *module)
         return NULL;
     }
 
+    /*
+    ** If the limit is too high (or RLIM_INFINITY), we might
+    ** allocate huge amounts of memory or even fail to allocate.
+    */
+    out_size = limit.rlim_cur;
+    if (out_size > DEVPOLL_MAX_OUT_BUFFER_SIZE) {
+        out_size = DEVPOLL_MAX_OUT_BUFFER_SIZE;
+    }
+
     fd_devpoll = _Py_open("/dev/poll", O_RDWR);
     if (fd_devpoll == -1)
         return NULL;
 
-    fds = PyMem_NEW(struct pollfd, limit.rlim_cur);
+    fds = PyMem_NEW(struct pollfd, DEVPOLL_IN_BUFFER_SIZE);
     if (fds == NULL) {
         close(fd_devpoll);
         PyErr_NoMemory();
         return NULL;
     }
 
+    out_fds = PyMem_NEW(struct pollfd, out_size);
+    if (fds == NULL) {
+        close(fd_devpoll);
+        PyMem_Free(fds);
+        PyErr_NoMemory();
+        return NULL;
+    }
+
     self = PyObject_New(devpollObject, get_select_state(module)->devpoll_Type);
     if (self == NULL) {
         close(fd_devpoll);
         PyMem_Free(fds);
+        PyMem_Free(out_fds);
         return NULL;
     }
     self->fd_devpoll = fd_devpoll;
-    self->max_n_fds = limit.rlim_cur;
     self->n_fds = 0;
     self->fds = fds;
+    self->out_size = out_size;
+    self->out_fds = out_fds;
 
     return self;
 }
@@ -1176,6 +1199,7 @@ devpoll_dealloc(PyObject *op)
     PyTypeObject *type = Py_TYPE(self);
     (void)devpoll_internal_close(self);
     PyMem_Free(self->fds);
+    PyMem_Free(self->out_fds);
     PyObject_Free(self);
     Py_DECREF(type);
 }