diff --git a/jedi/api/__init__.py b/jedi/api/__init__.py
index d72260f2..75bf964f 100644
--- a/jedi/api/__init__.py
+++ b/jedi/api/__init__.py
@@ -157,6 +157,7 @@ class Script(object):
             last word part. To ignore certain strange patterns with dots, just
             use regex.
             """
+
             if re.match('\d+\.\.$|\.{4}$', path):
                 return True  # check Ellipsis and float literal `1.`
 
@@ -164,8 +165,9 @@ class Script(object):
 
         debug.speed('completions start')
         path = self._user_context.get_path_until_cursor()
-        if not completion_possible(path):
-            return []
+        # TODO still needed with the new parser?
+        #if not completion_possible(path):
+        #    return []
         path, dot, like = helpers.completion_parts(path)
 
         user_stmt = self._parser.user_stmt_with_whitespace()
diff --git a/jedi/api/helpers.py b/jedi/api/helpers.py
index 7baf7609..c69fd1ca 100644
--- a/jedi/api/helpers.py
+++ b/jedi/api/helpers.py
@@ -36,24 +36,30 @@ def get_on_import_stmt(evaluator, user_context, user_stmt, is_like_search=False)
 
 def check_error_statements(evaluator, module, pos):
     for error_statement in module.error_statement_stacks:
-        if error_statement.first_type in ('import_from' or 'import_name') \
+        if error_statement.first_type in ('import_from', 'import_name') \
                 and error_statement.first_pos < pos <= error_statement.next_start_pos:
             return importer_from_error_statement(evaluator, module, error_statement, pos)
     return None
 
 
 def importer_from_error_statement(evaluator, module, error_statement, pos):
+    def check_dotted(children):
+        for name in children[::2]:
+            if name.end_pos < pos:
+                yield name
+
     names = []
     level = 0
     for typ, nodes in error_statement.stack:
         if typ == 'dotted_name':
-            names += nodes[::2]
+            names += check_dotted(nodes)
         elif typ == 'import_from':
             for node in nodes:
                 if isinstance(node, pt.Node) and node.type == 'dotted_name':
-                    names += node.children[::2]
-        print(typ, nodes)
-
-    print('x', names)
+                    names += check_dotted(node.children[::2])
+                elif node in ('.', '...'):
+                    level += len(node.value)
+                elif isinstance(node, pt.Name) and node.end_pos < pos:
+                    names.append(node)
 
     return imports.get_importer(evaluator, names, module, level)
diff --git a/jedi/evaluate/imports.py b/jedi/evaluate/imports.py
index 9292ec10..ec3ff0ca 100644
--- a/jedi/evaluate/imports.py
+++ b/jedi/evaluate/imports.py
@@ -54,7 +54,8 @@ class ImportWrapper(pr.Base):
         module = self._import.get_parent_until()
         importer = get_importer(self._evaluator, tuple(import_path),
                                 module, self._import.level)
-        return importer.completion_names(self._evaluator)
+        only_modules = isinstance(self._import, pr.ImportName)
+        return importer.completion_names(self._evaluator, only_modules)
 
     @memoize_default()
     def follow(self, is_goto=False):
@@ -91,7 +92,7 @@ class ImportWrapper(pr.Base):
 
             # follow the rest of the import (not FS -> classes, functions)
             if len(rest) > 1 or rest and self.is_like_search:
-                if ('os', 'path') == importer.str_import_path()[:2] \
+                if ('os', 'path') == importer.str_import_path[:2] \
                         and self._import.level == 0:
                     # This is a huge exception, we follow a nested import
                     # ``os.path``, because it's a very important one in Python
@@ -443,7 +444,10 @@ class _Importer(object):
         return in_path + sys_path_with_modifications(self._evaluator, self.module)
 
     def follow(self, evaluator):
-        scope, rest = self.follow_file_system()
+        try:
+            scope, rest = self.follow_file_system()
+        except ModuleNotFound:
+            return []
         if rest:
             # follow the rest of the import (not FS -> classes, functions)
             return []
@@ -653,7 +657,6 @@ class _Importer(object):
                 if only_modules:
                     # In the case of an import like `from x.` we don't need to
                     # add all the variables.
-                    print(self.import_path)
                     if ('os',) == self.str_import_path and not self.level:
                         # os.path is a hardcoded exception, because it's a
                         # ``sys.modules`` modification.
diff --git a/test/completion/on_import.py b/test/completion/on_import.py
index a2ec198a..557bfaaa 100644
--- a/test/completion/on_import.py
+++ b/test/completion/on_import.py
@@ -71,6 +71,13 @@ from import_tree.p import pkg
 from .import_tree import 
 #? 10 ['run']
 from ..run import 
+#? ['run']
+from ..run
+#? 10 ['run']
+from ..run.
+#? []
+from ..run.
+
 #? ['run']
 from .. import run