diff --git a/jedi/api/completion.py b/jedi/api/completion.py
index 3078d83f4..674833404 100644
--- a/jedi/api/completion.py
+++ b/jedi/api/completion.py
@@ -683,14 +683,14 @@ def search_in_module(inference_state, module_context, names, wanted_names,
 def extract_imported_names(node):
     imported_names = []
 
-    if node.type in ['import_as_names', 'dotted_as_names', 'import_as_name']:
+    if node.type in ['import_as_names', 'dotted_as_names', 'dotted_as_name', 'import_as_name']:
         for index, child in enumerate(node.children):
             if child.type == 'name':
-                if (index > 0 and node.children[index - 1].type == "keyword"
+                if (index > 1 and node.children[index - 1].type == "keyword"
                         and node.children[index - 1].value == "as"):
                     continue
                 imported_names.append(child.value)
-            elif child.type == 'import_as_name':
+            elif child.type in ('import_as_name', 'dotted_as_name'):
                 imported_names.extend(extract_imported_names(child))
 
     return imported_names
diff --git a/test/test_inference/test_imports.py b/test/test_inference/test_imports.py
index 03de11827..dfec5cd45 100644
--- a/test/test_inference/test_imports.py
+++ b/test/test_inference/test_imports.py
@@ -318,9 +318,14 @@ def import_names(*args, **kwargs):
     s = 'from os import path, p'
     assert 'path' not in import_names(s)
     assert 'path' in import_names(s, column=len(s) - 3)
+    assert 'path' in import_names("from import path")
+    assert 'path' in import_names("from import chdir, path")
 
-    s = 'import path as pp, p'
-    assert 'path' not in import_names(s)
+    s = 'import math as mm, m'
+    assert 'math' not in import_names(s)
+
+    s = 'import math as os, o'
+    assert 'os' in import_names(s)
 
     s = 'from os import path as pp, p'
     assert 'path' not in import_names(s)