diff --git a/src/basic/parse-util.c b/src/basic/parse-util.c
index 15818958e4..7344dc4311 100644
--- a/src/basic/parse-util.c
+++ b/src/basic/parse-util.c
@@ -392,7 +392,7 @@ int safe_atou_full(const char *s, unsigned base, unsigned *ret_u) {
                 return -errno;
         if (!x || x == s || *x != 0)
                 return -EINVAL;
-        if (s[0] == '-')
+        if (l != 0 && s[0] == '-')
                 return -ERANGE;
         if ((unsigned long) (unsigned) l != l)
                 return -ERANGE;
@@ -451,7 +451,7 @@ int safe_atollu_full(const char *s, unsigned base, long long unsigned *ret_llu)
                 return -errno;
         if (!x || x == s || *x != 0)
                 return -EINVAL;
-        if (*s == '-')
+        if (l != 0 && s[0] == '-')
                 return -ERANGE;
 
         if (ret_llu)
@@ -493,7 +493,7 @@ int safe_atou8(const char *s, uint8_t *ret) {
                 return -errno;
         if (!x || x == s || *x != 0)
                 return -EINVAL;
-        if (s[0] == '-')
+        if (l != 0 && s[0] == '-')
                 return -ERANGE;
         if ((unsigned long) (uint8_t) l != l)
                 return -ERANGE;
@@ -530,7 +530,7 @@ int safe_atou16_full(const char *s, unsigned base, uint16_t *ret) {
                 return -errno;
         if (!x || x == s || *x != 0)
                 return -EINVAL;
-        if (s[0] == '-')
+        if (l != 0 && s[0] == '-')
                 return -ERANGE;
         if ((unsigned long) (uint16_t) l != l)
                 return -ERANGE;