diff --git a/src/basic/fd-util.c b/src/basic/fd-util.c
index cee20a9a81..6ed04449bf 100644
--- a/src/basic/fd-util.c
+++ b/src/basic/fd-util.c
@@ -177,9 +177,13 @@ int fd_cloexec(int fd, bool cloexec) {
 _pure_ static bool fd_in_set(int fd, const int fdset[], size_t n_fdset) {
         assert(n_fdset == 0 || fdset);
 
-        for (size_t i = 0; i < n_fdset; i++)
+        for (size_t i = 0; i < n_fdset; i++) {
+                if (fdset[i] < 0)
+                        continue;
+
                 if (fdset[i] == fd)
                         return true;
+        }
 
         return false;
 }
@@ -252,6 +256,10 @@ static int close_all_fds_special_case(const int except[], size_t n_except) {
         if (!have_close_range)
                 return 0;
 
+        if (n_except == 1 && except[0] < 0) /* Minor optimization: if we only got one fd, and it's invalid,
+                                             * we got none */
+                n_except = 0;
+
         switch (n_except) {
 
         case 0: