diff --git a/.travis.yml b/.travis.yml
index a8d48d0c7ce..71e8d262882 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -1,14 +1,29 @@
 language: php
 
 matrix:
-  include:
+  exclude:
     - php: 7.0
+      env: DEPS="" COVERALLS=true
     - php: 7.1
+      env: DEPS="" COVERALLS=true
     - php: 7.2
-      env: COVERALLS=true
+      env: DEPS="" COVERALLS=""
     - php: nightly
+      env: DEPS="" COVERALLS=true
   allow_failures:
     - php: nightly
+    - php: 7.0
+      env: DEPS="" COVERALLS=""
+php:
+  - 7.0
+  - 7.1
+  - 7.2
+  - nightly
+
+env:
+  - DEPS="--prefer-lowest --prefer-stable" COVERALLS=""
+  - DEPS="" COVERALLS=""
+  - DEPS="" COVERALLS=true
 
 cache:
   directories:
@@ -16,13 +31,14 @@ cache:
 
 before_install:
     # determine INI file
-    - export INI=~/.phpenv/versions/$(phpenv version-name)/etc/conf.d/travis.ini
+    - export INI_DIR=~/.phpenv/versions/$(phpenv version-name)/etc/conf.d
+    - export INI=$INI_DIR/travis.ini
     # disable default memory limit
     - echo memory_limit = 2G >> $INI
-    - if [[ $COVERALLS = "" ]]; then phpenv config-rm xdebug.ini; fi
+    - if [[ $COVERALLS = "" && -f $INI_DIR/xdebug.ini ]]; then phpenv config-rm xdebug.ini; fi
 
 install:
-  - composer --prefer-source install
+  - composer --prefer-source $DEPS update
 
 script:
   - vendor/bin/phpunit
diff --git a/composer.json b/composer.json
index f159f2c117d..7e117b3e216 100644
--- a/composer.json
+++ b/composer.json
@@ -32,7 +32,7 @@
         "optimize-autoloader": true
     },
     "require-dev": {
-        "phpunit/phpunit": "^5.7.4",
+        "phpunit/phpunit": "^6.0 || ^7.0",
         "squizlabs/php_codesniffer": "^3.0",
         "php-coveralls/php-coveralls": "^2.0",
         "bamarni/composer-bin-plugin": "^1.2"
diff --git a/tests/DocumentationTest.php b/tests/DocumentationTest.php
index 2a7fd98cab6..46a2abb5548 100644
--- a/tests/DocumentationTest.php
+++ b/tests/DocumentationTest.php
@@ -110,7 +110,7 @@ public function testAllIssuesCovered()
      */
     public function testInvalidCode($code, $error_message, $error_levels = [], $check_references = false)
     {
-        if (strpos($this->getName(), 'SKIPPED-') !== false) {
+        if (strpos($this->getTestName(), 'SKIPPED-') !== false) {
             $this->markTestSkipped();
         }
 
diff --git a/tests/FileManipulationTest.php b/tests/FileManipulationTest.php
index efe0cddd71b..c80db7c4ccf 100644
--- a/tests/FileManipulationTest.php
+++ b/tests/FileManipulationTest.php
@@ -33,7 +33,7 @@ public function setUp()
      */
     public function testValidCode($input_code, $output_code, $php_version, array $issues_to_fix, $safe_types)
     {
-        $test_name = $this->getName();
+        $test_name = $this->getTestName();
         if (strpos($test_name, 'PHP7-') !== false) {
             if (version_compare(PHP_VERSION, '7.0.0dev', '<')) {
                 $this->markTestSkipped('Test case requires PHP 7.');
diff --git a/tests/FileReferenceTest.php b/tests/FileReferenceTest.php
index a575d73962e..a4a5d11eb21 100644
--- a/tests/FileReferenceTest.php
+++ b/tests/FileReferenceTest.php
@@ -41,7 +41,7 @@ public function setUp()
      */
     public function testValidCode($input_code, $symbol, $expected_locations)
     {
-        $test_name = $this->getName();
+        $test_name = $this->getTestName();
         if (strpos($test_name, 'PHP7-') !== false) {
             if (version_compare(PHP_VERSION, '7.0.0dev', '<')) {
                 $this->markTestSkipped('Test case requires PHP 7.');
diff --git a/tests/TestCase.php b/tests/TestCase.php
index 986ec2adc07..16e12dbb698 100644
--- a/tests/TestCase.php
+++ b/tests/TestCase.php
@@ -4,6 +4,7 @@
 use PHPUnit\Framework\TestCase as BaseTestCase;
 use Psalm\Checker\FileChecker;
 use Psalm\Checker\ProjectChecker;
+use RuntimeException;
 
 class TestCase extends BaseTestCase
 {
@@ -99,4 +100,13 @@ public function analyzeFile($file_path, \Psalm\Context $context)
         );
         $file_checker->analyze($context);
     }
+    protected function getTestName(bool $withDataSet = true): string
+    {
+        $name = parent::getName($withDataSet);
+        /** @psalm-suppress DocblockTypeContradiction PHPUnit 7 introduced nullable name */
+        if (null === $name) {
+            throw new RuntimeException('anonymous test - shouldn\'t happen');
+        }
+        return $name;
+    }
 }
diff --git a/tests/Traits/FileCheckerInvalidCodeParseTestTrait.php b/tests/Traits/FileCheckerInvalidCodeParseTestTrait.php
index ffac8a6a30c..77a2634a5d9 100644
--- a/tests/Traits/FileCheckerInvalidCodeParseTestTrait.php
+++ b/tests/Traits/FileCheckerInvalidCodeParseTestTrait.php
@@ -24,7 +24,7 @@ abstract public function providerFileCheckerInvalidCodeParse();
      */
     public function testInvalidCode($code, $error_message, $error_levels = [], $strict_mode = false)
     {
-        if (strpos($this->getName(), 'SKIPPED-') !== false) {
+        if (strpos($this->getTestName(), 'SKIPPED-') !== false) {
             $this->markTestSkipped();
         }
 
diff --git a/tests/Traits/FileCheckerValidCodeParseTestTrait.php b/tests/Traits/FileCheckerValidCodeParseTestTrait.php
index 0594a51d982..abac5f4d557 100644
--- a/tests/Traits/FileCheckerValidCodeParseTestTrait.php
+++ b/tests/Traits/FileCheckerValidCodeParseTestTrait.php
@@ -26,7 +26,7 @@ abstract public function providerFileCheckerValidCodeParse();
      */
     public function testValidCode($code, $assertions = [], $error_levels = [], $scope_vars = [])
     {
-        $test_name = $this->getName();
+        $test_name = $this->getTestName();
         if (strpos($test_name, 'PHP7-') !== false) {
             if (version_compare(PHP_VERSION, '7.0.0dev', '<')) {
                 $this->markTestSkipped('Test case requires PHP 7.');
diff --git a/tests/UnusedCodeTest.php b/tests/UnusedCodeTest.php
index c8b631761f7..627957cc444 100644
--- a/tests/UnusedCodeTest.php
+++ b/tests/UnusedCodeTest.php
@@ -40,7 +40,7 @@ public function setUp()
      */
     public function testValidCode($code, array $error_levels = [])
     {
-        $test_name = $this->getName();
+        $test_name = $this->getTestName();
         if (strpos($test_name, 'PHP7-') !== false) {
             if (version_compare(PHP_VERSION, '7.0.0dev', '<')) {
                 $this->markTestSkipped('Test case requires PHP 7.');
@@ -81,7 +81,7 @@ public function testValidCode($code, array $error_levels = [])
      */
     public function testInvalidCode($code, $error_message, $error_levels = [])
     {
-        if (strpos($this->getName(), 'SKIPPED-') !== false) {
+        if (strpos($this->getTestName(), 'SKIPPED-') !== false) {
             $this->markTestSkipped();
         }
 
diff --git a/tests/UnusedVariableTest.php b/tests/UnusedVariableTest.php
index 36cd06bd577..fde78c9af85 100644
--- a/tests/UnusedVariableTest.php
+++ b/tests/UnusedVariableTest.php
@@ -40,7 +40,7 @@ public function setUp()
      */
     public function testValidCode($code, array $error_levels = [])
     {
-        $test_name = $this->getName();
+        $test_name = $this->getTestName();
         if (strpos($test_name, 'PHP7-') !== false) {
             if (version_compare(PHP_VERSION, '7.0.0dev', '<')) {
                 $this->markTestSkipped('Test case requires PHP 7.');
@@ -81,7 +81,7 @@ public function testValidCode($code, array $error_levels = [])
      */
     public function testInvalidCode($code, $error_message, $error_levels = [])
     {
-        if (strpos($this->getName(), 'SKIPPED-') !== false) {
+        if (strpos($this->getTestName(), 'SKIPPED-') !== false) {
             $this->markTestSkipped();
         }