diff --git a/jedi/api.py b/jedi/api.py
index 3b49b40e..535df83a 100644
--- a/jedi/api.py
+++ b/jedi/api.py
@@ -108,6 +108,8 @@ class Script(object):
 
         debug.speed('complete start')
         path = self.module.get_path_until_cursor()
+        if re.search('^\.|\.\.$', path):
+            return []
         path, dot, like = self._get_completion_parts(path)
 
         try:
diff --git a/test/completion/basic.py b/test/completion/basic.py
index 526d1bbc..26d59cf7 100644
--- a/test/completion/basic.py
+++ b/test/completion/basic.py
@@ -9,6 +9,16 @@ int()
 int(str)
 
 
+# -----------------
+# should not complete
+# -----------------
+#? []
+.
+#? []
+str..
+#? []
+a(0):.
+
 # -----------------
 # if/else/elif
 # -----------------