diff --git a/src/basic/parse-util.c b/src/basic/parse-util.c
index b6358c459a..151067e916 100644
--- a/src/basic/parse-util.c
+++ b/src/basic/parse-util.c
@@ -67,11 +67,14 @@ int parse_mode(const char *s, mode_t *ret) {
         assert(s);
         assert(ret);
 
+        s += strspn(s, WHITESPACE);
+        if (s[0] == '-')
+                return -ERANGE;
+
         errno = 0;
         l = strtol(s, &x, 8);
         if (errno != 0)
                 return -errno;
-
         if (!x || x == s || *x)
                 return -EINVAL;
         if (l < 0 || l  > 07777)
@@ -162,15 +165,15 @@ int parse_size(const char *t, uint64_t base, uint64_t *size) {
                 unsigned i;
 
                 p += strspn(p, WHITESPACE);
-                if (*p == '-')
-                        return -ERANGE;
 
                 errno = 0;
                 l = strtoull(p, &e, 10);
-                if (errno > 0)
+                if (errno != 0)
                         return -errno;
                 if (e == p)
                         return -EINVAL;
+                if (*p == '-')
+                        return -ERANGE;
 
                 if (*e == '.') {
                         e++;
@@ -181,7 +184,7 @@ int parse_size(const char *t, uint64_t base, uint64_t *size) {
                                 char *e2;
 
                                 l2 = strtoull(e, &e2, 10);
-                                if (errno > 0)
+                                if (errno != 0)
                                         return -errno;
 
                                 /* Ignore failure. E.g. 10.M is valid */
@@ -307,12 +310,24 @@ int safe_atou(const char *s, unsigned *ret_u) {
         assert(s);
         assert(ret_u);
 
+        /* strtoul() is happy to parse negative values, and silently
+         * converts them to unsigned values without generating an
+         * error. We want a clean error, hence let's look for the "-"
+         * prefix on our own, and generate an error. But let's do so
+         * only after strtoul() validated that the string is clean
+         * otherwise, so that we return EINVAL preferably over
+         * ERANGE. */
+
+        s += strspn(s, WHITESPACE);
+
         errno = 0;
         l = strtoul(s, &x, 0);
-
-        if (!x || x == s || *x || errno)
-                return errno > 0 ? -errno : -EINVAL;
-
+        if (errno != 0)
+                return -errno;
+        if (!x || x == s || *x)
+                return -EINVAL;
+        if (s[0] == '-')
+                return -ERANGE;
         if ((unsigned long) (unsigned) l != l)
                 return -ERANGE;
 
@@ -329,10 +344,10 @@ int safe_atoi(const char *s, int *ret_i) {
 
         errno = 0;
         l = strtol(s, &x, 0);
-
-        if (!x || x == s || *x || errno)
-                return errno > 0 ? -errno : -EINVAL;
-
+        if (errno != 0)
+                return -errno;
+        if (!x || x == s || *x)
+                return -EINVAL;
         if ((long) (int) l != l)
                 return -ERANGE;
 
@@ -347,11 +362,16 @@ int safe_atollu(const char *s, long long unsigned *ret_llu) {
         assert(s);
         assert(ret_llu);
 
+        s += strspn(s, WHITESPACE);
+
         errno = 0;
         l = strtoull(s, &x, 0);
-
-        if (!x || x == s || *x || errno)
-                return errno ? -errno : -EINVAL;
+        if (errno != 0)
+                return -errno;
+        if (!x || x == s || *x)
+                return -EINVAL;
+        if (*s == '-')
+                return -ERANGE;
 
         *ret_llu = l;
         return 0;
@@ -366,9 +386,10 @@ int safe_atolli(const char *s, long long int *ret_lli) {
 
         errno = 0;
         l = strtoll(s, &x, 0);
-
-        if (!x || x == s || *x || errno)
-                return errno ? -errno : -EINVAL;
+        if (errno != 0)
+                return -errno;
+        if (!x || x == s || *x)
+                return -EINVAL;
 
         *ret_lli = l;
         return 0;
@@ -381,12 +402,16 @@ int safe_atou8(const char *s, uint8_t *ret) {
         assert(s);
         assert(ret);
 
+        s += strspn(s, WHITESPACE);
+
         errno = 0;
         l = strtoul(s, &x, 0);
-
-        if (!x || x == s || *x || errno)
-                return errno > 0 ? -errno : -EINVAL;
-
+        if (errno != 0)
+                return -errno;
+        if (!x || x == s || *x)
+                return -EINVAL;
+        if (s[0] == '-')
+                return -ERANGE;
         if ((unsigned long) (uint8_t) l != l)
                 return -ERANGE;
 
@@ -401,12 +426,16 @@ int safe_atou16(const char *s, uint16_t *ret) {
         assert(s);
         assert(ret);
 
+        s += strspn(s, WHITESPACE);
+
         errno = 0;
         l = strtoul(s, &x, 0);
-
-        if (!x || x == s || *x || errno)
-                return errno > 0 ? -errno : -EINVAL;
-
+        if (errno != 0)
+                return -errno;
+        if (!x || x == s || *x)
+                return -EINVAL;
+        if (s[0] == '-')
+                return -ERANGE;
         if ((unsigned long) (uint16_t) l != l)
                 return -ERANGE;
 
@@ -423,10 +452,10 @@ int safe_atoi16(const char *s, int16_t *ret) {
 
         errno = 0;
         l = strtol(s, &x, 0);
-
-        if (!x || x == s || *x || errno)
-                return errno > 0 ? -errno : -EINVAL;
-
+        if (errno != 0)
+                return -errno;
+        if (!x || x == s || *x)
+                return -EINVAL;
         if ((long) (int16_t) l != l)
                 return -ERANGE;
 
@@ -448,10 +477,13 @@ int safe_atod(const char *s, double *ret_d) {
 
         errno = 0;
         d = strtod_l(s, &x, loc);
-
-        if (!x || x == s || *x || errno) {
+        if (errno != 0) {
                 freelocale(loc);
-                return errno ? -errno : -EINVAL;
+                return -errno;
+        }
+        if (!x || x == s || *x) {
+                freelocale(loc);
+                return -EINVAL;
         }
 
         freelocale(loc);