diff --git a/src/archive.rs b/src/archive.rs
index e875124a..e6628006 100644
--- a/src/archive.rs
+++ b/src/archive.rs
@@ -217,12 +217,17 @@ impl Archive<dyn Read + '_> {
         for entry in self._entries(None)? {
             let mut file = entry.map_err(|e| TarError::new("failed to iterate over archive", e))?;
             if file.header().entry_type() == crate::EntryType::Directory {
-                directories.push(file);
+                directories.push((file.path()?.components().count(), file));
             } else {
                 file.unpack_in(dst)?;
             }
         }
-        for mut dir in directories {
+
+        // Work from leaves up.  Otherwise when a parent directory has
+        // no write permission, any empty subdirectories beneath it
+        // cannot be created.
+        directories.sort_by(|a, b| b.0.cmp(&a.0));
+        for (_, mut dir) in directories {
             dir.unpack_in(dst)?;
         }
 
diff --git a/tests/all.rs b/tests/all.rs
index fa38ef62..4abcab57 100644
--- a/tests/all.rs
+++ b/tests/all.rs
@@ -1317,6 +1317,32 @@ fn read_only_directory_containing_files() {
     assert!(ar.unpack(td.path()).is_ok());
 }
 
+#[test]
+fn read_only_directory_containing_empty_directory() {
+    let test_dirs_with_modes: Box<dyn Fn(&[(&str, u32)])> = Box::new(|dirs| {
+        let td = t!(TempBuilder::new().prefix("tar-rs").tempdir());
+
+        let mut b = Builder::new(Vec::<u8>::new());
+
+        for (path, mode) in dirs {
+            let mut h = Header::new_gnu();
+            t!(h.set_path(path));
+            h.set_size(0);
+            h.set_entry_type(EntryType::dir());
+            h.set_mode(*mode);
+            h.set_cksum();
+            t!(b.append(&h, "".as_bytes()));
+        }
+
+        let contents = t!(b.into_inner());
+        let mut ar = Archive::new(&contents[..]);
+        assert!(ar.unpack(td.path()).is_ok());
+    });
+
+    test_dirs_with_modes(&[("dir/", 0o444), ("dir/subdir", 0o755)]);
+    test_dirs_with_modes(&[("dir/subdir", 0o755), ("dir/", 0o444)]);
+}
+
 // This test was marked linux only due to macOS CI can't handle `set_current_dir` correctly
 #[test]
 #[cfg(target_os = "linux")]