diff --git a/.travis.yml b/.travis.yml
index 03b7ecb..290df75 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -1,15 +1,25 @@
 language: php
 
 php:
-  - 5.3
+# - 5.3 # requires old distro, see below
   - 5.4
   - 5.5
   - 5.6
   - 7
   - hhvm
 
+# lock distro so new future defaults will not break the build
+dist: trusty
+
+matrix:
+  include:
+    - php: 5.3
+      dist: precise
+
+sudo: false
+
 install:
-  - composer install --prefer-source --no-interaction
+  - composer install --no-interaction
   
 script:
   - ./vendor/bin/phpunit --coverage-text
diff --git a/README.md b/README.md
index c426e21..03f5eda 100644
--- a/README.md
+++ b/README.md
@@ -23,6 +23,7 @@ provide alternate implementations.
   * [Fallback get](#fallback-get)
   * [Fallback-get-and-set](#fallback-get-and-set)
 * [Install](#install)
+* [Tests](#tests)
 * [License](#license)
 
 ## Usage
@@ -150,6 +151,21 @@ $ composer require "react/cache:~0.4.0|~0.3.0"
 
 More details and upgrade guides can be found in the [CHANGELOG](CHANGELOG.md).
 
+## Tests
+
+To run the test suite, you first need to clone this repo and then install all
+dependencies [through Composer](https://getcomposer.org):
+
+```bash
+$ composer install
+```
+
+To run the test suite, go to the project root and run:
+
+```bash
+$ php vendor/bin/phpunit
+```
+
 ## License
 
 MIT, see [LICENSE file](LICENSE).
diff --git a/composer.json b/composer.json
index 854099f..9a8bb33 100644
--- a/composer.json
+++ b/composer.json
@@ -14,6 +14,6 @@
         "psr-4": { "React\\Tests\\Cache\\": "tests/" }
     },
     "require-dev": {
-        "phpunit/phpunit": "~4.8"
+        "phpunit/phpunit": "^6.4 || ^5.7 || ^4.8.35"
     }
 }
diff --git a/tests/TestCase.php b/tests/TestCase.php
index 93a04fb..aa449f2 100644
--- a/tests/TestCase.php
+++ b/tests/TestCase.php
@@ -2,7 +2,9 @@
 
 namespace React\Tests\Cache;
 
-class TestCase extends \PHPUnit_Framework_TestCase
+use PHPUnit\Framework\TestCase as BaseTestCase;
+
+class TestCase extends BaseTestCase
 {
     protected function expectCallableExactly($amount)
     {
@@ -36,6 +38,6 @@ protected function expectCallableNever()
 
     protected function createCallableMock()
     {
-        return $this->getMock('React\Tests\Cache\CallableStub');
+        return $this->getMockBuilder('React\Tests\Cache\CallableStub')->getMock();
     }
 }