diff --git a/jedi/utils.py b/jedi/utils.py
index 2da56cf8..41bc2da5 100644
--- a/jedi/utils.py
+++ b/jedi/utils.py
@@ -9,13 +9,51 @@ from jedi import Interpreter
 
 class JediRLCompleter(Completer):
 
+    def _jedi_matches(self, text):
+        completions = Interpreter(text, [self.namespace]).completions()
+        return [text + c.complete for c in completions]
+
+    @staticmethod
+    def _split_for_default_matcher(text, delims='()'):
+        """
+        Split `text` before passing it to :meth:`Completer.attr_matches` etc.
+
+        >>> JediRLCompleter._split_for_default_matcher('f(')
+        ('f(', '')
+        >>> JediRLCompleter._split_for_default_matcher('f().g')
+        ('f()', '.g')
+
+        """
+        import re
+        m = re.match(r"(.*[{0}])([^{0}]*)".format(re.escape(delims)), text)
+        if not m:
+            return ('', text)
+        return m.groups()
+
+    def _find_matches(self, default_matcher, text):
+        """
+        Common part for :meth:`attr_matches` and :meth:`global_matches`.
+
+        Try `default_matcher` first and return what it returns if
+        it is not empty.  Otherwise, try :meth:`_jedi_matches`.
+
+        :arg default_matcher: :meth:`.Completer.attr_matches` or
+                              :meth:`.Completer.global_matches`.
+        :arg str text: code to complete
+        """
+        (pre, body) = self._split_for_default_matcher(text)
+        matches = default_matcher(self, body)
+        if matches:
+            return [pre + m for m in matches]
+        return self._jedi_matches(text)
+
     def attr_matches(self, text):
-        if '(' in text or ')' in text:
-            completions = Interpreter(text, [self.namespace]).completions()
-            return [text + c.complete for c in completions]
-        else:
-            # NOTE: Completer is old type class
-            return Completer.attr_matches(self, text)
+        # NOTE: Completer is old type class so `super` cannot be used here
+        return self._find_matches(Completer.attr_matches, text)
+
+    def global_matches(self, text):
+        # NOTE: Completer is old type class so `super` cannot be used here
+        return self._find_matches(Completer.global_matches, text)
 
 
 def setup_readline():