diff --git a/Lib/test/test_signal.py b/Lib/test/test_signal.py
index ab42ed7..aa2b8bb 100644
--- a/Lib/test/test_signal.py
+++ b/Lib/test/test_signal.py
@@ -611,6 +611,15 @@
         # and the handler should have been called
         self.assertEqual(self.hndl_called, True)
 
+    def test_setitimer_tiny(self):
+        # bpo-30807: C setitimer() takes a microsecond-resolution interval.
+        # Check that float -> timeval conversion doesn't round
+        # the interval down to zero, which would disable the timer.
+        self.itimer = signal.ITIMER_REAL
+        signal.setitimer(self.itimer, 1e-6)
+        time.sleep(1)
+        self.assertEqual(self.hndl_called, True)
+
 
 class PendingSignalsTests(unittest.TestCase):
     """
diff --git a/Misc/NEWS.d/next/Library/2017-06-29-22-04-44.bpo-30807.sLtjY-.rst b/Misc/NEWS.d/next/Library/2017-06-29-22-04-44.bpo-30807.sLtjY-.rst
new file mode 100644
index 0000000..ce6f48a
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2017-06-29-22-04-44.bpo-30807.sLtjY-.rst
@@ -0,0 +1,6 @@
+signal.setitimer() may disable the timer when passed a tiny value.
+
+Tiny values (such as 1e-6) are valid non-zero values for setitimer(), which
+is specified as taking microsecond-resolution intervals. However, on some
+platform, our conversion routine could convert 1e-6 into a zero interval,
+therefore disabling the timer instead of (re-)scheduling it.
diff --git a/Modules/signalmodule.c b/Modules/signalmodule.c
index ed2f4e8..55e4c2a 100644
--- a/Modules/signalmodule.c
+++ b/Modules/signalmodule.c
@@ -139,6 +139,10 @@
 {
     tv->tv_sec = floor(d);
     tv->tv_usec = fmod(d, 1.0) * 1000000.0;
+    /* Don't disable the timer if the computation above rounds down to zero. */
+    if (d > 0.0 && tv->tv_sec == 0 && tv->tv_usec == 0) {
+        tv->tv_usec = 1;
+    }
 }
 
 Py_LOCAL_INLINE(double)