diff --git a/Misc/ACKS b/Misc/ACKS
index 3b8c7f29502..6e7dfe4a8de 100644
--- a/Misc/ACKS
+++ b/Misc/ACKS
@@ -41,6 +41,7 @@ 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 19a3e9330bc..62fe05d50cb 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -849,6 +849,9 @@ 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.
 
 - Issue #16593: Have BSD 'make -s' do the right thing, thanks to Daniel Shahaf
diff --git a/Modules/selectmodule.c b/Modules/selectmodule.c
index 3f846d807ae..7863aaa4bbd 100644
--- a/Modules/selectmodule.c
+++ b/Modules/selectmodule.c
@@ -1743,7 +1743,7 @@ 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 */
     {0,         0},     /* sentinel */
@@ -1788,7 +1788,7 @@ 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) {