diff --git a/jedi/api/project.py b/jedi/api/project.py
index dfcc7ff2..95c1ca23 100644
--- a/jedi/api/project.py
+++ b/jedi/api/project.py
@@ -328,7 +328,8 @@ class Project:
             )
 
         # 2. Search for identifiers in the project.
-        for module_context in search_in_file_ios(inference_state, file_ios, name):
+        for module_context in search_in_file_ios(inference_state, file_ios,
+                                                 name, complete=complete):
             names = get_module_names(module_context.tree_node, all_scopes=all_scopes)
             names = [module_context.create_name(n) for n in names]
             names = _remove_imports(names)
diff --git a/jedi/inference/references.py b/jedi/inference/references.py
index df47dabb..6ffa160e 100644
--- a/jedi/inference/references.py
+++ b/jedi/inference/references.py
@@ -282,12 +282,13 @@ def get_module_contexts_containing_name(inference_state, module_contexts, name,
                                   limit_reduction=limit_reduction)
 
 
-def search_in_file_ios(inference_state, file_io_iterator, name, limit_reduction=1):
+def search_in_file_ios(inference_state, file_io_iterator, name,
+                       limit_reduction=1, complete=False):
     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')
+    regex = re.compile(r'\b' + re.escape(name) + (r'' if complete else r'\b'))
     for file_io in file_io_iterator:
         file_io_count += 1
         m = _check_fs(inference_state, file_io, regex)
diff --git a/test/test_api/test_project.py b/test/test_api/test_project.py
index 9ca4686c..f2a5e991 100644
--- a/test/test_api/test_project.py
+++ b/test/test_api/test_project.py
@@ -68,6 +68,10 @@ def test_load_save_project(tmpdir):
          dict(all_scopes=True)),
         ('some_search_test_var', ['test_api.test_project.test_search.some_search_test_var'],
          dict(complete=True, all_scopes=True)),
+        # Make sure that the searched name is not part of the file, by
+        # splitting it up.
+        ('some_search_test_v' + 'a', ['test_api.test_project.test_search.some_search_test_var'],
+         dict(complete=True, all_scopes=True)),
 
         ('sample_int', ['helpers.sample_int'], {}),
         ('sample_int', ['helpers.sample_int'], dict(all_scopes=True)),
@@ -146,7 +150,7 @@ def test_search(string, full_names, kwargs):
         defs = project.complete_search(string, **kwargs)
     else:
         defs = project.search(string, **kwargs)
-    assert sorted([('stub:' if d.is_stub() else '') + d.full_name for d in defs]) == full_names
+    assert sorted([('stub:' if d.is_stub() else '') + (d.full_name or d.name) for d in defs]) == full_names
 
 
 @pytest.mark.parametrize(