diff --git a/.travis.yml b/.travis.yml
index b31b114c..18014285 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -5,15 +5,11 @@ python:
   - 3.8
   - 3.7
   - 3.6
-  - 3.5
-  - 2.7
 
 env:
   - JEDI_TEST_ENVIRONMENT=38
   - JEDI_TEST_ENVIRONMENT=37
   - JEDI_TEST_ENVIRONMENT=36
-  - JEDI_TEST_ENVIRONMENT=35
-  - JEDI_TEST_ENVIRONMENT=27
   - JEDI_TEST_ENVIRONMENT=interpreter
 
 matrix:
diff --git a/appveyor.yml b/appveyor.yml
index a68fa11e..12d72d3d 100644
--- a/appveyor.yml
+++ b/appveyor.yml
@@ -6,25 +6,12 @@ environment:
   - TOXENV: py37
     PYTHON_PATH: C:\Python37
     JEDI_TEST_ENVIRONMENT: 36
-  - TOXENV: py37
-    PYTHON_PATH: C:\Python37
-    JEDI_TEST_ENVIRONMENT: 35
-  - TOXENV: py37
-    PYTHON_PATH: C:\Python37
-    JEDI_TEST_ENVIRONMENT: 27
 
   - TOXENV: py36
     PYTHON_PATH: C:\Python36
     JEDI_TEST_ENVIRONMENT: 37
   - TOXENV: py36
     PYTHON_PATH: C:\Python36
-    JEDI_TEST_ENVIRONMENT: 36
-  - TOXENV: py36
-    PYTHON_PATH: C:\Python36
-    JEDI_TEST_ENVIRONMENT: 35
-  - TOXENV: py36
-    PYTHON_PATH: C:\Python36
-    JEDI_TEST_ENVIRONMENT: 27
 
   - TOXENV: py35
     PYTHON_PATH: C:\Python35
@@ -32,25 +19,6 @@ environment:
   - TOXENV: py35
     PYTHON_PATH: C:\Python35
     JEDI_TEST_ENVIRONMENT: 36
-  - TOXENV: py35
-    PYTHON_PATH: C:\Python35
-    JEDI_TEST_ENVIRONMENT: 35
-  - TOXENV: py35
-    PYTHON_PATH: C:\Python35
-    JEDI_TEST_ENVIRONMENT: 27
-
-  - TOXENV: py27
-    PYTHON_PATH: C:\Python27
-    JEDI_TEST_ENVIRONMENT: 37
-  - TOXENV: py27
-    PYTHON_PATH: C:\Python27
-    JEDI_TEST_ENVIRONMENT: 36
-  - TOXENV: py27
-    PYTHON_PATH: C:\Python27
-    JEDI_TEST_ENVIRONMENT: 35
-  - TOXENV: py27
-    PYTHON_PATH: C:\Python27
-    JEDI_TEST_ENVIRONMENT: 27
 install:
   - git submodule update --init --recursive
   - set PATH=%PYTHON_PATH%;%PYTHON_PATH%\Scripts;%PATH%
diff --git a/setup.py b/setup.py
index 131d0473..84d79624 100755
--- a/setup.py
+++ b/setup.py
@@ -33,12 +33,12 @@ setup(name='jedi',
       keywords='python completion refactoring vim',
       long_description=readme,
       packages=find_packages(exclude=['test', 'test.*']),
-      python_requires='>=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*, !=3.4.*',
+      python_requires='>=3.6',
       install_requires=install_requires,
       extras_require={
           'testing': [
               # Pytest 5 doesn't support Python 2 anymore.
-              'pytest>=3.9.0,<5.0.0',
+              'pytest<6.0.0',
               # docopt for sith doctests
               'docopt',
               # coloroma for colored debug output
@@ -58,10 +58,7 @@ setup(name='jedi',
           'Intended Audience :: Developers',
           'License :: OSI Approved :: MIT License',
           'Operating System :: OS Independent',
-          'Programming Language :: Python :: 2',
-          'Programming Language :: Python :: 2.7',
           'Programming Language :: Python :: 3',
-          'Programming Language :: Python :: 3.5',
           'Programming Language :: Python :: 3.6',
           'Programming Language :: Python :: 3.7',
           'Programming Language :: Python :: 3.8',