diff --git a/jedi/api/__init__.py b/jedi/api/__init__.py
index 246af06f..4ab5e7b0 100644
--- a/jedi/api/__init__.py
+++ b/jedi/api/__init__.py
@@ -131,30 +131,33 @@ class Script(object):
         :rtype: list of :class:`classes.Completion`
         """
         def get_completions(user_stmt, bs):
-            if user_stmt is None:
-                module = self._parser.module()
-                importer, only_modules = helpers.check_error_statements(
-                    self._evaluator, module, self._pos
-                )
-                #print(importer.completion_names(self._evaluator, True))
-                if importer is not None:
-                    names = importer.completion_names(self._evaluator, only_modules)
-                    return [(name, module) for name in names]
-            elif isinstance(user_stmt, pr.Import):
+            module = self._parser.module()
+            importer, only_modules = helpers.check_error_statements(
+                self._evaluator, module, self._pos
+            )
+            completions = []
+            #print(importer.completion_names(self._evaluator, True))
+            if importer is not None:
+                names = importer.completion_names(self._evaluator, only_modules)
+                completions = [(name, module) for name in 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
-                if next(context) == 'from':
+                if False and next(context) == 'from':
                     # completion is just "import" if before stands from ..
-                    return ((k, bs) for k in keywords.keyword_names('import'))
+                    completions += ((k, bs) for k in keywords.keyword_names('import'))
 
                 module = self._parser.module()
                 name = user_stmt.name_for_position(self._pos)
                 imp = imports.ImportWrapper(self._evaluator, name)
-                return [(n, module) for n in imp.get_defined_names()]
+                completions += [(n, module) for n in imp.completions()]
 
+            if importer or isinstance(user_stmt, pr.Import):
+                return completions
             return self._simple_complete(path, dot, like)
 
+
         debug.speed('completions start')
         path = self._user_context.get_path_until_cursor()
         # dots following an int are not the start of a completion but a float
diff --git a/jedi/evaluate/imports.py b/jedi/evaluate/imports.py
index 02680d59..96645f0c 100644
--- a/jedi/evaluate/imports.py
+++ b/jedi/evaluate/imports.py
@@ -47,13 +47,17 @@ class ImportWrapper(pr.Base):
         self.import_path = self._import.path_for_name(name)
         self.is_like_search = False       # TODO REMOVE
 
-    def get_defined_names(self):
+    def completions(self):
         # The import path needs to be reduced by one, because we're completing.
         import_path = self.import_path[:-1]
         module = self._import.get_parent_until()
         importer = get_importer(self._evaluator, tuple(import_path),
                                 module, self._import.level)
-        only_modules = isinstance(self._import, pr.ImportName)
+        if isinstance(self._import, pr.ImportFrom):
+            c = self._import.children
+            only_modules = c[c.index('import')].start_pos >= self._name.start_pos
+        else:
+            only_modules = True
         return importer.completion_names(self._evaluator, only_modules)
 
     @memoize_default()
diff --git a/test/completion/on_import.py b/test/completion/on_import.py
index 557bfaaa..76b45fb9 100644
--- a/test/completion/on_import.py
+++ b/test/completion/on_import.py
@@ -25,6 +25,8 @@ import classes
 
 #? ['timedelta']
 from datetime import timedel
+#? 21 []
+from datetime.timedel import timedel
 
 # should not be possible, because names can only be looked up 1 level deep.
 #? []
@@ -59,7 +61,9 @@ import datetime.
 #? []
 import datetime.date
 
-#? 18 ['import']
+#? 17 ['import']
+from import_tree import pkg
+#? 18 ['import', 'pkg']
 from import_tree. import pkg
 #? 17 ['mod1', 'mod2', 'random', 'pkg', 'rename1', 'rename2', 'recurse_class1', 'recurse_class2']
 from import_tree. import pkg