diff --git a/IPython/core/tests/test_completer.py b/IPython/core/tests/test_completer.py
index 8d6f4f0..777cf1e 100644
--- a/IPython/core/tests/test_completer.py
+++ b/IPython/core/tests/test_completer.py
@@ -783,6 +783,13 @@ def test_aimport_module_completer():
     nt.assert_in('io', matches)
     nt.assert_not_in('int', matches)
 
+def test_nested_import_module_completer():
+    ip = get_ipython()
+    _, matches = ip.complete(None, 'import IPython.co', 17)
+    nt.assert_in('IPython.core', matches)
+    nt.assert_not_in('import IPython.core', matches)
+    nt.assert_not_in('IPython.display', matches)
+
 def test_import_module_completer():
     ip = get_ipython()
     _, matches = ip.complete('i', 'import i')