diff --git a/conftest.py b/conftest.py
index 89d096d9..a45f1e3d 100644
--- a/conftest.py
+++ b/conftest.py
@@ -1,6 +1,7 @@
 import tempfile
 import shutil
 import os
+import sys
 
 import pytest
 
@@ -87,3 +88,14 @@ def environment():
         return get_default_environment()
 
     return get_python_environment('python%s.%s' % tuple(version))
+
+
+@pytest.fixture(scope='session')
+def has_typing(environment):
+    if environment.version_info >= (3, 5, 0):
+        # This if is just needed to avoid that tests ever skip way more than
+        # they should for all Python versions.
+        return True
+
+    script = jedi.Script('import typing', environment=environment)
+    return bool(script.goto_definitions())
diff --git a/test/test_integration.py b/test/test_integration.py
index 93446493..7df1e81e 100644
--- a/test/test_integration.py
+++ b/test/test_integration.py
@@ -31,9 +31,11 @@ unspecified = %s
 """ % (case, sorted(d - a), sorted(a - d))
 
 
-def test_completion(case, monkeypatch, environment):
+def test_completion(case, monkeypatch, environment, has_typing):
     if case.skip is not None:
         pytest.skip(case.skip)
+    if not has_typing and 'typing' in case.path:
+        pytest.skip('Needs the typing module installed to run this test.')
     repo_root = helpers.root_dir
     monkeypatch.chdir(os.path.join(repo_root, 'jedi'))
     case.run(assert_case_equal, environment)