diff --git a/Doc/library/select.rst b/Doc/library/select.rst
index e252e7a..5ffb215 100644
--- a/Doc/library/select.rst
+++ b/Doc/library/select.rst
@@ -57,7 +57,16 @@
 
    (Only supported on Linux 2.5.44 and newer.) Return an edge polling object,
    which can be used as Edge or Level Triggered interface for I/O
-   events. *sizehint* and *flags* are deprecated and completely ignored.
+   events.
+
+   *sizehint* informs epoll about the expected number of events to be
+   registered.  It must be positive, or `-1` to use the default. It is only
+   used on older systems where :c:func:`epoll_create1` is not available;
+   otherwise it has no effect (though its value is still checked).
+
+   *flags* is deprecated and completely ignored.  However, when supplied, its
+   value must be ``0`` or ``select.EPOLL_CLOEXEC``, otherwise ``OSError`` is
+   raised.
 
    See the :ref:`epoll-objects` section below for the methods supported by
    epolling objects.
diff --git a/Lib/test/test_epoll.py b/Lib/test/test_epoll.py
index 549e0f7..efb54f4 100644
--- a/Lib/test/test_epoll.py
+++ b/Lib/test/test_epoll.py
@@ -74,11 +74,11 @@
         ep.close()
         self.assertTrue(ep.closed)
         self.assertRaises(ValueError, ep.fileno)
+
         if hasattr(select, "EPOLL_CLOEXEC"):
-            select.epoll(select.EPOLL_CLOEXEC).close()
+            select.epoll(-1, select.EPOLL_CLOEXEC).close()
             select.epoll(flags=select.EPOLL_CLOEXEC).close()
             select.epoll(flags=0).close()
-            self.assertRaises(OSError, select.epoll, flags=12356)
 
     def test_badcreate(self):
         self.assertRaises(TypeError, select.epoll, 1, 2, 3)
@@ -88,6 +88,13 @@
         self.assertRaises(TypeError, select.epoll, ['foo'])
         self.assertRaises(TypeError, select.epoll, {})
 
+        self.assertRaises(ValueError, select.epoll, 0)
+        self.assertRaises(ValueError, select.epoll, -2)
+        self.assertRaises(ValueError, select.epoll, sizehint=-2)
+
+        if hasattr(select, "EPOLL_CLOEXEC"):
+            self.assertRaises(OSError, select.epoll, flags=12356)
+
     def test_context_manager(self):
         with select.epoll(16) as ep:
             self.assertGreater(ep.fileno(), 0)
@@ -117,19 +124,19 @@
         try:
             # TypeError: argument must be an int, or have a fileno() method.
             self.assertRaises(TypeError, ep.register, object(),
-                select.EPOLLIN | select.EPOLLOUT)
+                              select.EPOLLIN | select.EPOLLOUT)
             self.assertRaises(TypeError, ep.register, None,
-                select.EPOLLIN | select.EPOLLOUT)
+                              select.EPOLLIN | select.EPOLLOUT)
             # ValueError: file descriptor cannot be a negative integer (-1)
             self.assertRaises(ValueError, ep.register, -1,
-                select.EPOLLIN | select.EPOLLOUT)
+                              select.EPOLLIN | select.EPOLLOUT)
             # OSError: [Errno 9] Bad file descriptor
             self.assertRaises(OSError, ep.register, 10000,
-                select.EPOLLIN | select.EPOLLOUT)
+                              select.EPOLLIN | select.EPOLLOUT)
             # registering twice also raises an exception
             ep.register(server, select.EPOLLIN | select.EPOLLOUT)
             self.assertRaises(OSError, ep.register, server,
-                select.EPOLLIN | select.EPOLLOUT)
+                              select.EPOLLIN | select.EPOLLOUT)
         finally:
             ep.close()
 
@@ -160,9 +167,9 @@
 
         ep = select.epoll(16)
         ep.register(server.fileno(),
-                   select.EPOLLIN | select.EPOLLOUT | select.EPOLLET)
+                    select.EPOLLIN | select.EPOLLOUT | select.EPOLLET)
         ep.register(client.fileno(),
-                   select.EPOLLIN | select.EPOLLOUT | select.EPOLLET)
+                    select.EPOLLIN | select.EPOLLOUT | select.EPOLLET)
 
         now = time.monotonic()
         events = ep.poll(1, 4)
diff --git a/Misc/NEWS.d/next/Library/2018-06-21-09-33-02.bpo-32568.f_meGY.rst b/Misc/NEWS.d/next/Library/2018-06-21-09-33-02.bpo-32568.f_meGY.rst
new file mode 100644
index 0000000..3ade8cf
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2018-06-21-09-33-02.bpo-32568.f_meGY.rst
@@ -0,0 +1,2 @@
+Make select.epoll() and its documentation consistent regarding *sizehint* and
+*flags*.
diff --git a/Modules/selectmodule.c b/Modules/selectmodule.c
index 3b7713a..d6b8fc1 100644
--- a/Modules/selectmodule.c
+++ b/Modules/selectmodule.c
@@ -1297,14 +1297,17 @@
 static PyObject *
 pyepoll_new(PyTypeObject *type, PyObject *args, PyObject *kwds)
 {
-    int flags = 0, sizehint = FD_SETSIZE - 1;
+    int flags = 0, sizehint = -1;
     static char *kwlist[] = {"sizehint", "flags", NULL};
 
     if (!PyArg_ParseTupleAndKeywords(args, kwds, "|ii:epoll", kwlist,
                                      &sizehint, &flags))
         return NULL;
-    if (sizehint < 0) {
-        PyErr_SetString(PyExc_ValueError, "negative sizehint");
+    if (sizehint == -1) {
+        sizehint = FD_SETSIZE - 1;
+    }
+    else if (sizehint <= 0) {
+        PyErr_SetString(PyExc_ValueError, "sizehint must be positive or -1");
         return NULL;
     }
 
@@ -1314,7 +1317,6 @@
         return NULL;
     }
 #endif
-
     return newPyEpoll_Object(type, sizehint, -1);
 }