diff --git a/src/basic/fileio.c b/src/basic/fileio.c
index 20d3f567c9..ea607f8cfb 100644
--- a/src/basic/fileio.c
+++ b/src/basic/fileio.c
@@ -1319,8 +1319,7 @@ int tempfn_random_child(const char *p, const char *extra, char **ret) {
                 r = tmp_dir(&p);
                 if (r < 0)
                         return r;
-        } else if (isempty(p))
-                return -EINVAL;
+        }
 
         extra = strempty(extra);
 
@@ -1328,7 +1327,10 @@ int tempfn_random_child(const char *p, const char *extra, char **ret) {
         if (!t)
                 return -ENOMEM;
 
-        x = stpcpy(stpcpy(stpcpy(t, p), "/.#"), extra);
+        if (isempty(p))
+                x = stpcpy(stpcpy(t, ".#"), extra);
+        else
+                x = stpcpy(stpcpy(stpcpy(t, p), "/.#"), extra);
 
         u = random_u64();
         for (i = 0; i < 16; i++) {