diff --git a/Misc/NEWS.d/next/Library/2021-09-22-23-56-15.bpo-21302.vvQ3Su.rst b/Misc/NEWS.d/next/Library/2021-09-22-23-56-15.bpo-21302.vvQ3Su.rst
new file mode 100644
index 00000000000000..52ee8d7cc64f15
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2021-09-22-23-56-15.bpo-21302.vvQ3Su.rst
@@ -0,0 +1 @@
+In Unix operating systems, :func:`time.sleep` now uses the ``nanosleep()`` function, if ``clock_nanosleep()`` is not available but ``nanosleep()`` is available. ``nanosleep()`` allows to sleep with nanosecond precision.
\ No newline at end of file
diff --git a/Modules/timemodule.c b/Modules/timemodule.c
index 53ec86eb3981ef..aaf96e3f938682 100644
--- a/Modules/timemodule.c
+++ b/Modules/timemodule.c
@@ -2057,6 +2057,8 @@ pysleep(_PyTime_t secs)
 #ifndef MS_WINDOWS
 #ifdef HAVE_CLOCK_NANOSLEEP
     struct timespec timeout_abs;
+#elif defined(HAVE_NANOSLEEP)
+    struct timespec timeout;
 #else
     struct timeval timeout;
 #endif
@@ -2074,7 +2076,11 @@ pysleep(_PyTime_t secs)
 #endif
 
     do {
-#ifndef HAVE_CLOCK_NANOSLEEP
+#if defined(HAVE_NANOSLEEP) && !defined(HAVE_CLOCK_NANOSLEEP)
+        if (_PyTime_AsTimespec(secs, &timeout) < 0) {
+            return -1;
+        }
+#elif !defined(HAVE_CLOCK_NANOSLEEP)
         if (_PyTime_AsTimeval(secs, &timeout, _PyTime_ROUND_CEILING) < 0) {
             return -1;
         }
@@ -2088,7 +2094,11 @@ pysleep(_PyTime_t secs)
         err = ret;
 #else
         Py_BEGIN_ALLOW_THREADS
+#ifdef HAVE_NANOSLEEP
+        ret = nanosleep(&timeout, NULL);
+#else
         ret = select(0, (fd_set *)0, (fd_set *)0, (fd_set *)0, &timeout);
+#endif
         Py_END_ALLOW_THREADS
         err = errno;
 #endif
diff --git a/configure b/configure
index 2e3c9ba7baddd4..4acf91f22107f4 100755
--- a/configure
+++ b/configure
@@ -13310,6 +13310,64 @@ fi
 done
 
 
+for ac_func in nanosleep
+do :
+  ac_fn_c_check_func "$LINENO" "nanosleep" "ac_cv_func_nanosleep"
+if test "x$ac_cv_func_nanosleep" = xyes; then :
+  cat >>confdefs.h <<_ACEOF
+#define HAVE_NANOSLEEP 1
+_ACEOF
+
+else
+
+    { $as_echo "$as_me:${as_lineno-$LINENO}: checking for nanosleep in -lrt" >&5
+$as_echo_n "checking for nanosleep in -lrt... " >&6; }
+if ${ac_cv_lib_rt_nanosleep+:} false; then :
+  $as_echo_n "(cached) " >&6
+else
+  ac_check_lib_save_LIBS=$LIBS
+LIBS="-lrt  $LIBS"
+cat confdefs.h - <<_ACEOF >conftest.$ac_ext
+/* end confdefs.h.  */
+
+/* Override any GCC internal prototype to avoid an error.
+   Use char because int might match the return type of a GCC
+   builtin and then its argument prototype would still apply.  */
+#ifdef __cplusplus
+extern "C"
+#endif
+char nanosleep ();
+int
+main ()
+{
+return nanosleep ();
+  ;
+  return 0;
+}
+_ACEOF
+if ac_fn_c_try_link "$LINENO"; then :
+  ac_cv_lib_rt_nanosleep=yes
+else
+  ac_cv_lib_rt_nanosleep=no
+fi
+rm -f core conftest.err conftest.$ac_objext \
+    conftest$ac_exeext conftest.$ac_ext
+LIBS=$ac_check_lib_save_LIBS
+fi
+{ $as_echo "$as_me:${as_lineno-$LINENO}: result: $ac_cv_lib_rt_nanosleep" >&5
+$as_echo "$ac_cv_lib_rt_nanosleep" >&6; }
+if test "x$ac_cv_lib_rt_nanosleep" = xyes; then :
+
+        $as_echo "#define HAVE_NANOSLEEP 1" >>confdefs.h
+
+
+fi
+
+
+fi
+done
+
+
 for ac_func in clock_getres
 do :
   ac_fn_c_check_func "$LINENO" "clock_getres" "ac_cv_func_clock_getres"
diff --git a/configure.ac b/configure.ac
index 4a0694c442f3f7..48d86ef79199e1 100644
--- a/configure.ac
+++ b/configure.ac
@@ -4121,6 +4121,12 @@ AC_CHECK_FUNCS(clock_nanosleep, [], [
     ])
 ])
 
+AC_CHECK_FUNCS(nanosleep, [], [
+    AC_CHECK_LIB(rt, nanosleep, [
+        AC_DEFINE(HAVE_NANOSLEEP, 1)
+    ])
+])
+
 AC_MSG_CHECKING(for major, minor, and makedev)
 AC_LINK_IFELSE([AC_LANG_PROGRAM([[
 #if defined(MAJOR_IN_MKDEV)
diff --git a/pyconfig.h.in b/pyconfig.h.in
index d6408e9415e2d0..23d7111b9f77e7 100644
--- a/pyconfig.h.in
+++ b/pyconfig.h.in
@@ -736,6 +736,9 @@
 /* Define to 1 if you have the `mremap' function. */
 #undef HAVE_MREMAP
 
+/* Define to 1 if you have the `nanosleep' function. */
+#undef HAVE_NANOSLEEP
+
 /* Define to 1 if you have the <ncurses.h> header file. */
 #undef HAVE_NCURSES_H