diff --git a/.travis.yml b/.travis.yml
index 4e64346d5..23f60ae69 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -1,24 +1,31 @@
-sudo: false
+dist: xenial
+sudo: true
 language: python
+python: 3.7
 
 matrix:
   include:
-    - python: "3.6-dev"
-      env: TEST_CMD="flake8"
-    - python: "3.6"
-      env: TEST_CMD="./tests/pytype_test.py --num-parallel=4"
-    - python: "3.5-dev"
+    - name: "pytype"
+      python: 3.6
+      env:
+        - TEST_CMD="./tests/pytype_test.py --num-parallel=4"
+        - INSTALL="test"
+    - name: "mypy"
+      env:
+        - TEST_CMD="./tests/mypy_test.py"
+        - INSTALL="mypy"
+    - name: "mypy self test"
       env: TEST_CMD="./tests/mypy_selftest.py"
-    - python: "3.5"
-      env: TEST_CMD="./tests/mypy_test.py"
-    - python: "3.4"
+    - name: "check file consistency"
       env: TEST_CMD="./tests/check_consistent.py"
+    - name: "flake8"
+      env:
+        - TEST_CMD="flake8"
+        - INSTALL="test"
 
 install:
-  # pytype needs py-3.6, mypy needs py-3.3+. Additional logic in runtests.py
-  - if [[ $TRAVIS_PYTHON_VERSION == '3.6-dev' ]]; then pip install -r requirements-tests-py3.txt; fi
-  - if [[ $TRAVIS_PYTHON_VERSION == '3.6' ]]; then pip install -r requirements-tests-py3.txt; fi
-  - if [[ $TRAVIS_PYTHON_VERSION == '3.5' ]]; then pip install -U git+git://github.com/python/mypy git+git://github.com/python/typed_ast; fi
+  - if [[ $INSTALL == 'test' ]]; then pip install -r requirements-tests-py3.txt; fi
+  - if [[ $INSTALL == 'mypy' ]]; then pip install -U git+git://github.com/python/mypy git+git://github.com/python/typed_ast; fi
 
 script:
   - $TEST_CMD