diff --git a/jedi/api/completion.py b/jedi/api/completion.py
index 934b29d6..76771669 100644
--- a/jedi/api/completion.py
+++ b/jedi/api/completion.py
@@ -589,6 +589,7 @@ def search_in_module(inference_state, module_context, names, wanted_names,
                     module_context,
                     n.infer()
                 )
+        debug.dbg('dot lookup on search %s from %s', new_names, names[:10])
         names = new_names
 
     last_name = wanted_names[-1].lower()
diff --git a/jedi/api/project.py b/jedi/api/project.py
index 5d947cf3..49c335f4 100644
--- a/jedi/api/project.py
+++ b/jedi/api/project.py
@@ -5,6 +5,7 @@ import sys
 
 from jedi._compatibility import FileNotFoundError, PermissionError, \
     IsADirectoryError, scandir
+from jedi import debug
 from jedi.api.environment import get_cached_default_environment, create_environment
 from jedi.api.exceptions import WrongVersion
 from jedi.api.completion import search_in_module
@@ -15,8 +16,6 @@ from jedi.inference.imports import load_module_from_path, \
 from jedi.inference.sys_path import discover_buildout_paths
 from jedi.inference.cache import inference_state_as_method_param_cache
 from jedi.inference.references import recurse_find_python_folders_and_files, search_in_file_ios
-from jedi.inference.value.module import ModuleValue
-from jedi.inference import InferenceState
 from jedi.file_io import FolderIO, FileIO
 from jedi.common.utils import traverse_parents
 
@@ -189,6 +188,7 @@ class Project(object):
             raise NotImplementedError(
                 "No support for refactorings/search on Python 2/3.5"
             )
+        debug.dbg('Search for string %s', string)
         wanted_type, wanted_names = split_search_string(string)
         name = wanted_names[0]
 
@@ -219,6 +219,7 @@ class Project(object):
                 else:
                     continue
 
+            debug.dbg('Search of a specific module %s', m)
             for x in search_in_module(
                 inference_state,
                 m,
@@ -250,7 +251,6 @@ class Project(object):
             # folders.
             if not p.startswith(self._path)
         ]
-
         names = list(iter_module_names(inference_state, empty_module_context, sys_path))
         for x in search_in_module(
             inference_state,
@@ -258,7 +258,7 @@ class Project(object):
             names=names,
             wanted_type=wanted_type,
             wanted_names=wanted_names,
-            complete=complete
+            complete=complete,
         ):
             yield x  # Python 2...
 
diff --git a/jedi/inference/imports.py b/jedi/inference/imports.py
index 91887f99..c1ec688d 100644
--- a/jedi/inference/imports.py
+++ b/jedi/inference/imports.py
@@ -428,13 +428,19 @@ def import_module(inference_state, import_names, parent_module_value, sys_path):
 
 def _load_python_module(inference_state, file_io,
                         import_names=None, is_package=False):
+    is_stub = file_io.path.endswith('.pyi')
     module_node = inference_state.parse(
         file_io=file_io,
         cache=True,
         diff_cache=settings.fast_parser,
-        cache_path=settings.cache_directory
+        cache_path=settings.cache_directory,
+        use_latest_grammar=is_stub,
     )
 
+    from jedi.inference.gradual.typeshed import create_stub_module
+    if is_stub:
+        return create_stub_module(
+            inference_state, NO_VALUES, module_node, file_io, import_names)
     from jedi.inference.value import ModuleValue
     return ModuleValue(
         inference_state, module_node,
diff --git a/jedi/inference/sys_path.py b/jedi/inference/sys_path.py
index 5234ac2c..81b14624 100644
--- a/jedi/inference/sys_path.py
+++ b/jedi/inference/sys_path.py
@@ -207,7 +207,7 @@ def _get_buildout_script_paths(search_path):
 
 
 def remove_python_path_suffix(path):
-    for suffix in all_suffixes():
+    for suffix in all_suffixes() + ['.pyi']:
         if path.endswith(suffix):
             path = path[:-len(suffix)]
             break
diff --git a/test/test_api/test_project.py b/test/test_api/test_project.py
index e6d27847..b86d5813 100644
--- a/test/test_api/test_project.py
+++ b/test/test_api/test_project.py
@@ -89,10 +89,21 @@ def test_load_save_project(tmpdir):
           'examples.implicit_namespace_package.ns2'],
          dict(complete=True)),
 
+        # With namespace & stub
+        ('with_python.module', ['examples.stub_packages.with_python.module'], {}),
+        ('with_python.modul', ['examples.stub_packages.with_python.module'],
+         dict(complete=True)),
+        ('no_python.module', ['stub:examples.stub_packages.no_python.module'], {}),
+        ('no_python.modul', ['stub:examples.stub_packages.no_python.module'],
+         dict(complete=True)),
+        ('with_python-stubs.module', ['stub:examples.stub_packages.with_python-stubs.module'], {}),
+        ('no_python-stubs.module', ['stub:examples.stub_packages.no_python-stubs.module'], {}),
+
         # On sys path
         ('sys.path', ['stub:sys.path'], {}),
         ('json.dumps', ['stub:json.dumps', 'json.dumps'], {}),  # stdlib + stub
-        ('multiprocessing', ['stub:multiprocessing'], {})
+        ('multiprocessing', ['stub:multiprocessing'], {}),
+        ('multiprocessin', ['stub:multiprocessing'], dict(complete=True)),
     ]
 )
 @pytest.mark.skipif(sys.version_info < (3, 6), reason="Ignore Python 2, because EOL")