diff --git a/Lib/test/test_time.py b/Lib/test/test_time.py
index 8c1d8f8..d4f7d80 100644
--- a/Lib/test/test_time.py
+++ b/Lib/test/test_time.py
@@ -233,6 +233,15 @@
         t1 = time.mktime(lt1)
         self.assertTrue(0 <= (t1-t0) < 0.2)
 
+    def test_mktime(self):
+        # Issue #1726687
+        for t in (-2, -1, 0, 1):
+            try:
+                tt = time.localtime(t)
+            except (OverflowError, ValueError):
+                pass
+            self.assertEqual(time.mktime(tt), t)
+
 class TestLocale(unittest.TestCase):
     def setUp(self):
         self.oldloc = locale.setlocale(locale.LC_ALL)
diff --git a/Modules/timemodule.c b/Modules/timemodule.c
index 29b4eea..8c40d21 100644
--- a/Modules/timemodule.c
+++ b/Modules/timemodule.c
@@ -703,8 +703,11 @@
     time_t tt;
     if (!gettmarg(tup, &buf))
         return NULL;
+    buf.tm_wday = -1;  /* sentinel; original value ignored */
     tt = mktime(&buf);
-    if (tt == (time_t)(-1)) {
+    /* Return value of -1 does not necessarily mean an error, but tm_wday
+     * cannot remain set to -1 if mktime succedded. */
+    if (tt == (time_t)(-1) && buf.tm_wday == -1) {
         PyErr_SetString(PyExc_OverflowError,
                         "mktime argument out of range");
         return NULL;