diff --git a/jedi/api/__init__.py b/jedi/api/__init__.py
index 66c17043..73c2187b 100644
--- a/jedi/api/__init__.py
+++ b/jedi/api/__init__.py
@@ -141,19 +141,22 @@ class Script(object):
                 i = imports.get_importer(self._evaluator, imp_names, module, level)
                 c_names = i.completion_names(self._evaluator, only_modules)
                 completions = [(name, module) for name in c_names]
-            if isinstance(user_stmt, pr.Import):
-                # TODO this paragraph is necessary, but not sure it works.
-                context = self._user_context.get_context()
-                next(context)  # skip the path
+
+            # TODO this paragraph is necessary, but not sure it works.
+            context = self._user_context.get_context()
+            
+            print(next(self._user_context.get_context()), 'x')
+            if not next(context).startswith('.'):  # skip the path
                 if next(context) == 'from':
                     # completion is just "import" if before stands from ..
                     completions += ((k, bs) for k in keywords.keyword_names('import'))
+                    return completions
 
+            if isinstance(user_stmt, pr.Import):
                 module = self._parser.module()
-                name = user_stmt.name_for_position(self._pos)
-                if name is not None:
-                    imp = imports.ImportWrapper(self._evaluator, name)
-                    completions += [(n, module) for n in imp.completion_names()]
+                completion_names = imports.completion_names(self._evaluator,
+                                                            user_stmt, self._pos)
+                return completions + [(n, module) for n in completion_names]
 
             if names is None and not isinstance(user_stmt, pr.Import):
                 if not path and not dot:
diff --git a/jedi/api/helpers.py b/jedi/api/helpers.py
index 2d0b41f6..f1f2c992 100644
--- a/jedi/api/helpers.py
+++ b/jedi/api/helpers.py
@@ -59,13 +59,15 @@ def importer_from_error_statement(error_statement, pos):
                 return None, 0, False
         elif typ == 'import_from':
             for node in nodes:
-                if isinstance(node, pt.Node) and node.type == 'dotted_name':
+                if node.start_pos >= pos:
+                    break
+                elif isinstance(node, pt.Node) and node.type == 'dotted_name':
                     names += check_dotted(node.children)
                 elif node in ('.', '...'):
                     level += len(node.value)
-                elif isinstance(node, pt.Name) and node.start_pos <= pos:
+                elif isinstance(node, pt.Name):
                     names.append(node)
-                elif node == 'import' and node.start_pos <= pos:
+                elif node == 'import':
                     only_modules = False
 
     return names, level, only_modules
diff --git a/jedi/evaluate/imports.py b/jedi/evaluate/imports.py
index 401b2423..2ceb92fe 100644
--- a/jedi/evaluate/imports.py
+++ b/jedi/evaluate/imports.py
@@ -37,6 +37,33 @@ class ModuleNotFound(Exception):
         self.name_part = name_part
 
 
+def completion_names(evaluator, imp, pos):
+    name = imp.name_for_position(pos)
+    module = imp.get_parent_until()
+    if name is None:
+        level = 0
+        for node in imp.children:
+            if node.end_pos <= pos:
+                if node in ('.', '...'):
+                    level += len(node.value)
+            print(node, level)
+        import_path = []
+    else:
+        # Completion on an existing name.
+
+        # The import path needs to be reduced by one, because we're completing.
+        import_path = imp.path_for_name(name)[:-1]
+        level = imp.level
+
+    importer = get_importer(evaluator, tuple(import_path), module, level)
+    if isinstance(imp, pr.ImportFrom):
+        c = imp.children
+        only_modules = c[c.index('import')].start_pos >= pos
+    else:
+        only_modules = True
+    return importer.completion_names(evaluator, only_modules)
+
+
 class ImportWrapper(pr.Base):
     GlobalNamespace = 'TODO PLEASE DELETE ME'
     def __init__(self, evaluator, name):
diff --git a/test/test_integration_import.py b/test/test_integration_import.py
index 9ae6f57f..ca6f37b8 100644
--- a/test/test_integration_import.py
+++ b/test/test_integration_import.py
@@ -16,11 +16,22 @@ def test_goto_definition_on_import():
 
 @cwd_at('jedi')
 def test_complete_on_empty_import():
+    assert Script("from datetime import").completions()[0].name == 'import'
     # should just list the files in the directory
     assert 10 < len(Script("from .", path='').completions()) < 30
-    assert 10 < len(Script("from . import", 1, 5, '').completions()) < 30
-    assert 10 < len(Script("from . import classes", 1, 5, '').completions()) < 30
-    assert len(Script("import").completions()) == 0
+
+    # Global import
+    assert len(Script("from . import", 1, 5, '').completions()) > 30
+    # relative import
+    assert 10 < len(Script("from . import", 1, 6, '').completions()) < 30
+
+    # Global import
+    assert len(Script("from . import classes", 1, 5, '').completions()) > 30
+    # relative import
+    assert 10 < len(Script("from . import classes", 1, 6, '').completions()) < 30
+
+    wanted = set(['ImportError', 'import', 'ImportWarning'])
+    assert set([c.name for c in Script("import").completions()]) == wanted
     if not is_py26:  # python 2.6 doesn't always come with a library `import*`.
         assert len(Script("import import", path='').completions()) > 0