diff --git a/src/shared/time-util.c b/src/shared/time-util.c
index 43448e0c630..13d57ba5cd7 100644
--- a/src/shared/time-util.c
+++ b/src/shared/time-util.c
@@ -284,11 +284,32 @@ void dual_timestamp_deserialize(const char *value, dual_timestamp *t) {
 }
 
 int parse_timestamp(const char *t, usec_t *usec) {
+        static const struct {
+                const char *name;
+                const int nr;
+        } day_nr[] = {
+                { "Sunday",    0 },
+                { "Sun",       0 },
+                { "Monday",    1 },
+                { "Mon",       1 },
+                { "Tuesday",   2 },
+                { "Tue",       2 },
+                { "Wednesday", 3 },
+                { "Wed",       3 },
+                { "Thursday",  4 },
+                { "Thu",       4 },
+                { "Friday",    5 },
+                { "Fri",       5 },
+                { "Saturday",  6 },
+                { "Sat",       6 },
+        };
+
         const char *k;
         struct tm tm, copy;
         time_t x;
         usec_t plus = 0, minus = 0, ret;
-        int r;
+        int r, weekday = -1;
+        unsigned i;
 
         /*
          * Allowed syntaxes:
@@ -360,6 +381,21 @@ int parse_timestamp(const char *t, usec_t *usec) {
                 goto finish;
         }
 
+        for (i = 0; i < ELEMENTSOF(day_nr); i++) {
+                size_t skip;
+
+                if (!startswith_no_case(t, day_nr[i].name))
+                        continue;
+
+                skip = strlen(day_nr[i].name);
+                if (t[skip] != ' ')
+                        continue;
+
+                weekday = day_nr[i].nr;
+                t += skip + 1;
+                break;
+        }
+
         copy = tm;
         k = strptime(t, "%y-%m-%d %H:%M:%S", &tm);
         if (k && *k == 0)
@@ -417,6 +453,9 @@ finish:
         if (x == (time_t) -1)
                 return -EINVAL;
 
+        if (weekday >= 0 && tm.tm_wday != weekday)
+                return -EINVAL;
+
         ret = (usec_t) x * USEC_PER_SEC;
 
         ret += plus;
diff --git a/src/test/test-date.c b/src/test/test-date.c
index 7e14d196c69..40ffc17b2f7 100644
--- a/src/test/test-date.c
+++ b/src/test/test-date.c
@@ -19,54 +19,43 @@
   along with systemd; If not, see <http://www.gnu.org/licenses/>.
 ***/
 
+#include <string.h>
+
 #include "util.h"
 
+static void test_one(const char *p) {
+        usec_t t, q;
+        char buf[FORMAT_TIMESTAMP_MAX], buf_relative[FORMAT_TIMESTAMP_RELATIVE_MAX];
+
+        assert_se(parse_timestamp(p, &t) >= 0);
+        log_info("%s", format_timestamp(buf, sizeof(buf), t));
+
+        /* Chop off timezone */
+        *strrchr(buf, ' ') = 0;
+
+        assert_se(parse_timestamp(buf, &q) >= 0);
+        assert_se(q == t);
+
+        log_info("%s", strna(format_timestamp_relative(buf_relative, sizeof(buf_relative), t)));
+        assert_se(parse_timestamp(buf, &q) >= 0);
+}
+
 int main(int argc, char *argv[]) {
-
-        usec_t t;
-        char buf[FORMAT_TIMESTAMP_MAX];
-
-        assert_se(parse_timestamp("17:41", &t) >= 0);
-        log_info("%s", format_timestamp(buf, sizeof(buf), t));
-
-        assert_se(parse_timestamp("18:42:44", &t) >= 0);
-        log_info("%s", format_timestamp(buf, sizeof(buf), t));
-
-        assert_se(parse_timestamp("12-10-02 12:13:14", &t) >= 0);
-        log_info("%s", format_timestamp(buf, sizeof(buf), t));
-
-        assert_se(parse_timestamp("12-10-2 12:13:14", &t) >= 0);
-        log_info("%s", format_timestamp(buf, sizeof(buf), t));
-
-        assert_se(parse_timestamp("12-10-03 12:13", &t) >= 0);
-        log_info("%s", format_timestamp(buf, sizeof(buf), t));
-
-        assert_se(parse_timestamp("2012-12-30 18:42", &t) >= 0);
-        log_info("%s", format_timestamp(buf, sizeof(buf), t));
-
-        assert_se(parse_timestamp("2012-10-02", &t) >= 0);
-        log_info("%s", format_timestamp(buf, sizeof(buf), t));
-
-        assert_se(parse_timestamp("now", &t) >= 0);
-        log_info("%s", format_timestamp(buf, sizeof(buf), t));
-
-        assert_se(parse_timestamp("yesterday", &t) >= 0);
-        log_info("%s", format_timestamp(buf, sizeof(buf), t));
-
-        assert_se(parse_timestamp("today", &t) >= 0);
-        log_info("%s", format_timestamp(buf, sizeof(buf), t));
-
-        assert_se(parse_timestamp("tomorrow", &t) >= 0);
-        log_info("%s", format_timestamp(buf, sizeof(buf), t));
-
-        assert_se(parse_timestamp("+2d", &t) >= 0);
-        log_info("%s", format_timestamp(buf, sizeof(buf), t));
-
-        assert_se(parse_timestamp("+2y 4d", &t) >= 0);
-        log_info("%s", format_timestamp(buf, sizeof(buf), t));
-
-        assert_se(parse_timestamp("5months ago", &t) >= 0);
-        log_info("%s", format_timestamp(buf, sizeof(buf), t));
+        test_one("17:41");
+        test_one("18:42:44");
+        test_one("12-10-02 12:13:14");
+        test_one("12-10-2 12:13:14");
+        test_one("12-10-03 12:13");
+        test_one("2012-12-30 18:42");
+        test_one("2012-10-02");
+        test_one("Tue 2012-10-02");
+        test_one("now");
+        test_one("yesterday");
+        test_one("today");
+        test_one("tomorrow");
+        test_one("+2d");
+        test_one("+2y 4d");
+        test_one("5months ago");
 
         return 0;
 }