diff --git a/Doc/library/time.rst b/Doc/library/time.rst
index 817f5a5..63d45fd 100644
--- a/Doc/library/time.rst
+++ b/Doc/library/time.rst
@@ -226,11 +226,15 @@
    The earliest date for which it can generate a time is platform-dependent.
 
 
-.. function:: monotonic()
+.. function:: steady()
 
-   Monotonic non-decreasing clock. The clock is not related to the system clock
-   and cannot go backward.  The reference point of the returned
-   value is undefined so only the difference of consecutive calls is valid.
+   .. index::
+      single: benchmarking
+
+   Return the current time as a floating point number expressed in seconds.
+   This clock advances at a steady rate relative to real time and it may not be
+   adjusted. The reference point of the returned value is undefined so only the
+   difference of consecutive calls is valid.
 
    .. versionadded:: 3.3
 
@@ -547,20 +551,6 @@
       ('EET', 'EEST')
 
 
-.. function:: wallclock()
-
-   .. index::
-      single: Wallclock
-      single: benchmarking
-
-   Return the current time in fractions of a second to the system's best ability.
-   Use this when the most accurate representation of wall-clock is required, i.e.
-   when "processor time" is inappropriate.  The reference point of the returned
-   value is undefined so only the difference of consecutive calls is valid.
-
-   .. versionadded:: 3.3
-
-
 .. seealso::
 
    Module :mod:`datetime`
diff --git a/Doc/whatsnew/3.3.rst b/Doc/whatsnew/3.3.rst
index 84fdac1..ae7b3af 100644
--- a/Doc/whatsnew/3.3.rst
+++ b/Doc/whatsnew/3.3.rst
@@ -943,8 +943,7 @@
 
 * :func:`~time.clock_getres` and :func:`~time.clock_gettime` functions and
   ``CLOCK_xxx`` constants.
-* :func:`~time.monotonic`: monotonic clock.
-* :func:`~time.wallclock`.
+* :func:`~time.steady`.
 
 (Contributed by Victor Stinner in :issue:`10278`)
 
diff --git a/Lib/test/test_time.py b/Lib/test/test_time.py
index 1fc46aa..2baf066 100644
--- a/Lib/test/test_time.py
+++ b/Lib/test/test_time.py
@@ -331,29 +331,10 @@
             pass
         self.assertEqual(time.strftime('%Z', tt), tzname)
 
-    @unittest.skipUnless(hasattr(time, 'monotonic'),
-                         'need time.monotonic()')
-    def test_monotonic(self):
-        t1 = time.monotonic()
-        t2 = time.monotonic()
-        self.assertGreaterEqual(t2, t1)
-
-        t1 = time.monotonic()
+    def test_steady(self):
+        t1 = time.steady()
         time.sleep(0.1)
-        t2 = time.monotonic()
-        dt = t2 - t1
-        self.assertGreater(t2, t1)
-        self.assertAlmostEqual(dt, 0.1, delta=0.2)
-
-    def test_wallclock(self):
-        t1 = time.wallclock()
-        t2 = time.wallclock()
-        # may fail if the system clock was changed
-        self.assertGreaterEqual(t2, t1)
-
-        t1 = time.wallclock()
-        time.sleep(0.1)
-        t2 = time.wallclock()
+        t2 = time.steady()
         dt = t2 - t1
         # may fail if the system clock was changed
         self.assertGreater(t2, t1)
diff --git a/Modules/timemodule.c b/Modules/timemodule.c
index efebd49..c7efce6 100644
--- a/Modules/timemodule.c
+++ b/Modules/timemodule.c
@@ -769,63 +769,10 @@
 #endif /* HAVE_WORKING_TZSET */
 
 static PyObject *
-time_wallclock(PyObject *self, PyObject *unused)
+time_steady(PyObject *self, PyObject *unused)
 {
 #if defined(MS_WINDOWS) && !defined(__BORLANDC__)
     return win32_clock(1);
-#elif defined(HAVE_CLOCK_GETTIME) && defined(CLOCK_MONOTONIC)
-    static int clk_index = 0;
-    clockid_t clk_ids[] = {
-#ifdef CLOCK_MONOTONIC_RAW
-        CLOCK_MONOTONIC_RAW,
-#endif
-        CLOCK_MONOTONIC
-#ifdef CLOCK_REALTIME
-          /* On Linux, CLOCK_REALTIME uses the same clock than gettimeofday(),
-             but clock_gettime() has a nanosecond resolution. */
-        , CLOCK_REALTIME
-#endif
-    };
-    int ret;
-    struct timespec tp;
-
-    while (0 <= clk_index) {
-        clockid_t clk_id = clk_ids[clk_index];
-        ret = clock_gettime(clk_id, &tp);
-        if (ret == 0)
-            return PyFloat_FromDouble(tp.tv_sec + tp.tv_nsec * 1e-9);
-
-        clk_index++;
-        if (Py_ARRAY_LENGTH(clk_ids) <= clk_index)
-            clk_index = -1;
-    }
-    return time_time(self, NULL);
-#else
-    return time_time(self, NULL);
-#endif
-}
-
-PyDoc_STRVAR(wallclock_doc,
-"wallclock() -> float\n\
-\n\
-Return the current time in fractions of a second to the system's best\n\
-ability. Use this when the most accurate representation of wall-clock is\n\
-required, i.e. when \"processor time\" is inappropriate. The reference point\n\
-of the returned value is undefined so only the difference of consecutive\n\
-calls is valid.");
-
-#if (defined(MS_WINDOWS) && !defined(__BORLANDC__)) \
-    || (defined(HAVE_CLOCK_GETTIME) && defined(CLOCK_MONOTONIC)) \
-    || (defined(__APPLE__))
-#  define HAVE_PYTIME_MONOTONIC
-#endif
-
-#ifdef HAVE_PYTIME_MONOTONIC
-static PyObject *
-time_monotonic(PyObject *self, PyObject *unused)
-{
-#if defined(MS_WINDOWS) && !defined(__BORLANDC__)
-    return win32_clock(0);
 #elif defined(__APPLE__)
     uint64_t time = mach_absolute_time();
     double secs;
@@ -837,13 +784,14 @@
     secs = (double)time * timebase.numer / timebase.denom * 1e-9;
 
     return PyFloat_FromDouble(secs);
-#else
+#elif defined(HAVE_CLOCK_GETTIME)
     static int clk_index = 0;
     clockid_t clk_ids[] = {
 #ifdef CLOCK_MONOTONIC_RAW
         CLOCK_MONOTONIC_RAW,
 #endif
-        CLOCK_MONOTONIC
+        CLOCK_MONOTONIC,
+        CLOCK_REALTIME
     };
     int ret;
     struct timespec tp;
@@ -858,17 +806,20 @@
         if (Py_ARRAY_LENGTH(clk_ids) <= clk_index)
             clk_index = -1;
     }
-    PyErr_SetFromErrno(PyExc_OSError);
-    return NULL;
+    return time_time(self, NULL);
+#else
+    return time_time(self, NULL);
 #endif
 }
 
-PyDoc_STRVAR(monotonic_doc,
-"monotonic() -> float\n\
+PyDoc_STRVAR(steady_doc,
+"steady() -> float\n\
 \n\
-Monotonic clock. The reference point of the returned value is undefined so\n\
-only the difference of consecutive calls is valid.");
-#endif
+Return the current time as a floating point number expressed in seconds.\n\
+This clock advances at a steady rate relative to real time and it may not\n\
+be adjusted. The reference point of the returned value is undefined so only\n\
+the difference of consecutive calls is valid.");
+
 
 static void
 PyInit_timezone(PyObject *m) {
@@ -998,9 +949,7 @@
 #ifdef HAVE_MKTIME
     {"mktime",          time_mktime, METH_O, mktime_doc},
 #endif
-#ifdef HAVE_PYTIME_MONOTONIC
-    {"monotonic",       time_monotonic, METH_NOARGS, monotonic_doc},
-#endif
+    {"steady",          time_steady, METH_NOARGS, steady_doc},
 #ifdef HAVE_STRFTIME
     {"strftime",        time_strftime, METH_VARARGS, strftime_doc},
 #endif
@@ -1008,7 +957,6 @@
 #ifdef HAVE_WORKING_TZSET
     {"tzset",           time_tzset, METH_NOARGS, tzset_doc},
 #endif
-    {"wallclock",       time_wallclock, METH_NOARGS, wallclock_doc},
     {NULL,              NULL}           /* sentinel */
 };