diff --git a/tests/test_compat.py b/tests/test_compat.py
index ad58f64..90b67df 100644
--- a/tests/test_compat.py
+++ b/tests/test_compat.py
@@ -1,6 +1,7 @@
 from pydu.compat import (PY2, iterkeys, itervalues, iteritems,
                          text_type, string_types, numeric_types,
-                         is_iterable, has_next_attr)
+                         is_iterable, has_next_attr, urljoin,
+                         imap)
 
 
 def test_itersth():
@@ -51,4 +52,17 @@ def test_urlmisc():
 
 
 def test_imap():
-    from pydu.compat import imap
+    assert list(imap(pow, (2, 3, 10), (5, 2, 3))) == [32, 9, 1000]
+    assert list(imap(max, (1, 4, 7), (2, 3, 8))) == [2, 4, 8]
+
+
+# TODO: add test case
+def test_ulib():
+    from pydu.compat import ulib
+    pass
+
+
+# TODO: add test case
+def test_urlparse():
+    from pydu.compat import urlparse
+    pass
\ No newline at end of file
diff --git a/tests/test_string.py b/tests/test_string.py
index 44e738f..6715995 100644
--- a/tests/test_string.py
+++ b/tests/test_string.py
@@ -14,6 +14,9 @@ def test_safeunicode():
     assert safeunicode(1) == u'1'
     assert safeunicode('中文') == u'中文'
 
+    assert safeunicode(u'hello') == u'hello'
+    assert safeunicode(u'中文') == u'中文'
+
 
 def test_lstrips():
     assert lstrips('foobbar', '') == 'foobbar'