diff -r 09371221e59d Lib/test/test_signal.py
--- a/Lib/test/test_signal.py	Thu May 22 19:45:39 2014 +0100
+++ b/Lib/test/test_signal.py	Thu May 22 22:02:09 2014 +0200
@@ -56,6 +56,14 @@ class GenericTests(unittest.TestCase):
                 self.assertIsInstance(sig, signal.Signals)
                 self.assertEqual(sys.platform, "win32")
 
+    def test_nsig(self):
+        # Issue #20584: Ensure that NSIG is greater than all signal number
+        # exposed in Python
+        signals = (int(getattr(signal, name))
+                   for name in dir(signal)
+                   if (name.startswith("SIG") and not name.startswith('SIG_')))
+        self.assertLess(max(signals), signal.NSIG)
+
 
 @unittest.skipIf(sys.platform == "win32", "Not valid on Windows")
 class InterProcessSignalTests(unittest.TestCase):
diff -r 09371221e59d Modules/signalmodule.c
--- a/Modules/signalmodule.c	Thu May 22 19:45:39 2014 +0100
+++ b/Modules/signalmodule.c	Thu May 22 22:02:09 2014 +0200
@@ -37,6 +37,13 @@
 #define SIG_ERR ((PyOS_sighandler_t)(-1))
 #endif
 
+#if defined(_SIG_MAXSIG)
+   /* Issue #20584: On FreeBSD, NSIG is the number of "old signals" (ex: 32),
+      whereas _SIG_MAXSIG is the size of a sigset (ex: 128). */
+#  undef NSIG
+#  define NSIG _SIG_MAXSIG
+#endif
+
 #ifndef NSIG
 # if defined(_NSIG)
 #  define NSIG _NSIG            /* For BSD/SysV */