diff --git a/Misc/ACKS b/Misc/ACKS
index ae00e88e4ae..661d0ecaf36 100644
--- a/Misc/ACKS
+++ b/Misc/ACKS
@@ -45,6 +45,7 @@ Jon Anglin
 Heidi Annexstad
 Éric Araujo
 Alicia Arlen
+Jeffrey Armstrong
 Jason Asbahr
 David Ascher
 Chris AtLee
diff --git a/Misc/NEWS b/Misc/NEWS
index d7e01a7cabd..74d9840c914 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -517,6 +517,9 @@ Tests
 Build
 -----
 
+- Issue #16953: Fix socket module compilation on platforms with
+  HAVE_BROKEN_POLL. Patch by Jeffrey Armstrong.
+
 - Issue #16836: Enable IPv6 support even if IPv6 is disabled on the build host.
 
 - Cross compiling needs host and build settings. configure no longer
diff --git a/Modules/selectmodule.c b/Modules/selectmodule.c
index ce5ed477926..06abcf1ac3c 100644
--- a/Modules/selectmodule.c
+++ b/Modules/selectmodule.c
@@ -2098,7 +2098,7 @@ descriptors can be used.");
 
 static PyMethodDef select_methods[] = {
     {"select",          select_select,  METH_VARARGS,   select_doc},
-#ifdef HAVE_POLL
+#if defined(HAVE_POLL) && !defined(HAVE_BROKEN_POLL)
     {"poll",            select_poll,    METH_NOARGS,    poll_doc},
 #endif /* HAVE_POLL */
 #ifdef HAVE_SYS_DEVPOLL_H
@@ -2148,7 +2148,7 @@ PyInit_select(void)
     PyModule_AddIntConstant(m, "PIPE_BUF", PIPE_BUF);
 #endif
 
-#if defined(HAVE_POLL)
+#if defined(HAVE_POLL) && !defined(HAVE_BROKEN_POLL)
 #ifdef __APPLE__
     if (select_have_broken_poll()) {
         if (PyObject_DelAttrString(m, "poll") == -1) {