diff --git a/rmdir-empty b/rmdir-empty
index 774fff5..0cc0db2 100755
--- a/rmdir-empty
+++ b/rmdir-empty
@@ -7,9 +7,11 @@ rmdir_empty() {
     set -- .
   fi
 
-  find "$@" -depth \
-    -path "." -prune -or \
-    -type d -empty -exec rmdir -v {} \;
+  # do the first level directories first
+  for maxdepth_opt in "-maxdepth 1" ""; do
+    find "$@" -depth -mindepth 1 $maxdepth_opt \
+      -type d -empty -exec rmdir -v {} \;
+  done
 }
 
 rmdir_empty "$@"