diff --git a/src/basic/time-util.c b/src/basic/time-util.c
index 2eff230c68..81d3f3f38f 100644
--- a/src/basic/time-util.c
+++ b/src/basic/time-util.c
@@ -1,5 +1,6 @@
 /* SPDX-License-Identifier: LGPL-2.1+ */
 
+#include <ctype.h>
 #include <errno.h>
 #include <limits.h>
 #include <stdlib.h>
@@ -1023,7 +1024,8 @@ int parse_time(const char *t, usec_t *usec, usec_t default_unit) {
                 if (*e == '.') {
                         char *b = e + 1;
 
-                        if (*b == '-') /* Don't allow 0.-0 */
+                        /* Don't allow "0.-0", "3.+1" or "3. 1" */
+                        if (*b == '-' || *b == '+' || isspace(*b))
                                 return -EINVAL;
 
                         errno = 0;
@@ -1161,7 +1163,7 @@ int parse_nsec(const char *t, nsec_t *nsec) {
                 if (*e == '.') {
                         char *b = e + 1;
 
-                        if (*b == '-')
+                        if (*b == '-' || *b == '+' || isspace(*b))
                                 return -EINVAL;
 
                         errno = 0;
diff --git a/src/test/test-time-util.c b/src/test/test-time-util.c
index d7cb459e66..58c365df57 100644
--- a/src/test/test-time-util.c
+++ b/src/test/test-time-util.c
@@ -36,6 +36,8 @@ static void test_parse_sec(void) {
         assert_se(u == USEC_INFINITY);
         assert_se(parse_sec(" infinity ", &u) >= 0);
         assert_se(u == USEC_INFINITY);
+        assert_se(parse_sec("+3.1s", &u) >= 0);
+        assert_se(u == 3100 * USEC_PER_MSEC);
 
         assert_se(parse_sec(" xyz ", &u) < 0);
         assert_se(parse_sec("", &u) < 0);
@@ -50,6 +52,9 @@ static void test_parse_sec(void) {
         assert_se(parse_sec("3.-0s ", &u) < 0);
         assert_se(parse_sec(" infinity .7", &u) < 0);
         assert_se(parse_sec(".3 infinity", &u) < 0);
+        assert_se(parse_sec("3.+1s", &u) < 0);
+        assert_se(parse_sec("3. 1s", &u) < 0);
+        assert_se(parse_sec("3.s", &u) < 0);
 }
 
 static void test_parse_sec_fix_0(void) {
@@ -118,6 +123,8 @@ static void test_parse_nsec(void) {
         assert_se(u == NSEC_INFINITY);
         assert_se(parse_nsec(" infinity ", &u) >= 0);
         assert_se(u == NSEC_INFINITY);
+        assert_se(parse_nsec("+3.1s", &u) >= 0);
+        assert_se(u == 3100 * NSEC_PER_MSEC);
 
         assert_se(parse_nsec(" xyz ", &u) < 0);
         assert_se(parse_nsec("", &u) < 0);
@@ -126,6 +133,17 @@ static void test_parse_nsec(void) {
         assert_se(parse_nsec(".s ", &u) < 0);
         assert_se(parse_nsec(" infinity .7", &u) < 0);
         assert_se(parse_nsec(".3 infinity", &u) < 0);
+        assert_se(parse_nsec("-5s ", &u) < 0);
+        assert_se(parse_nsec("-0.3s ", &u) < 0);
+        assert_se(parse_nsec("-0.0s ", &u) < 0);
+        assert_se(parse_nsec("-0.-0s ", &u) < 0);
+        assert_se(parse_nsec("0.-0s ", &u) < 0);
+        assert_se(parse_nsec("3.-0s ", &u) < 0);
+        assert_se(parse_nsec(" infinity .7", &u) < 0);
+        assert_se(parse_nsec(".3 infinity", &u) < 0);
+        assert_se(parse_nsec("3.+1s", &u) < 0);
+        assert_se(parse_nsec("3. 1s", &u) < 0);
+        assert_se(parse_nsec("3.s", &u) < 0);
 }
 
 static void test_format_timespan_one(usec_t x, usec_t accuracy) {