diff --git a/jedi/api/project.py b/jedi/api/project.py
index f4cbd72a..e9f6b921 100644
--- a/jedi/api/project.py
+++ b/jedi/api/project.py
@@ -6,10 +6,13 @@ from jedi._compatibility import FileNotFoundError, PermissionError, IsADirectory
 from jedi._compatibility import scandir
 from jedi.api.environment import get_cached_default_environment, create_environment
 from jedi.api.exceptions import WrongVersion
+from jedi.api.classes import Definition
 from jedi._compatibility import force_unicode
 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_files
+from jedi.inference.references import recurse_find_python_files, search_in_file_ios
+from jedi.inference.helpers import get_module_names
+from jedi.inference import InferenceState
 from jedi.file_io import FolderIO
 from jedi.common.utils import traverse_parents
 
@@ -172,9 +175,11 @@ class Project(object):
         """
         Returns a generator of names
         """
-        for file_io in recurse_find_python_files(FolderIO(self._path)):
-            for name in get_names(all_scopes=True):
-                yield name
+        inference_state = InferenceState(self)
+        file_io_iterator = recurse_find_python_files(FolderIO(self._path))
+        for module_context in search_in_file_ios(inference_state, file_io_iterator, string):
+            for name in get_module_names(module_context.ree_node, all_scopes=all_scopes):
+                yield Definition(inference_state, module_context.create_name(name))
 
     def __repr__(self):
         return '<%s: %s>' % (self.__class__.__name__, self._path)
diff --git a/jedi/inference/references.py b/jedi/inference/references.py
index 53128dd0..0465ce75 100644
--- a/jedi/inference/references.py
+++ b/jedi/inference/references.py
@@ -3,6 +3,7 @@ import re
 
 from parso import python_bytes_to_unicode
 
+from jedi.debug import dbg
 from jedi.file_io import KnownContentFileIO
 from jedi.inference.imports import SubModuleName, load_module_from_path
 from jedi.inference.filters import ParserTreeFilter
@@ -254,19 +255,28 @@ def get_module_contexts_containing_name(inference_state, module_contexts, name,
     if len(name) <= 2:
         return
 
+    file_io_iterator = _find_python_files_in_sys_path(inference_state, module_contexts)
+    for x in search_in_file_ios(inference_state, file_io_iterator, name,
+                                limit_reduction=limit_reduction):
+        yield x  # Python 2...
+
+
+def search_in_file_ios(inference_state, file_io_iterator, name, limit_reduction=1):
     parse_limit = _PARSED_FILE_LIMIT / limit_reduction
     open_limit = _OPENED_FILE_LIMIT / limit_reduction
     file_io_count = 0
     parsed_file_count = 0
     regex = re.compile(r'\b' + re.escape(name) + r'\b')
-    for file_io in _find_python_files_in_sys_path(inference_state, module_contexts):
+    for file_io in file_io_iterator:
         file_io_count += 1
         m = _check_fs(inference_state, file_io, regex)
         if m is not None:
             parsed_file_count += 1
             yield m
             if parsed_file_count >= parse_limit:
+                dbg('Hit limit of parsed files: %s', parse_limit)
                 break
 
         if file_io_count >= open_limit:
+            dbg('Hit limit of opened files: %s', open_limit)
             break