diff --git a/.travis.yml b/.travis.yml
index 77c5ea3..bbca139 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -7,9 +7,6 @@ cache:
         - $HOME/.composer/cache/files
 
 php:
-    - 5.5
-    - 5.6
-    - 7.0
     - 7.1
     - 7.2
     - 7.3
@@ -24,18 +21,18 @@ branches:
         - /^analysis-.*$/
 
 matrix:
-    allow_failures:
-        - php: 7.3
     fast_finish: true
     include:
         - name: PHPSpec code coverage
-          php: 5.5
-          env: COMPOSER_FLAGS="--prefer-stable --prefer-lowest" COVERAGE=true TEST_COMMAND="composer test-ci" PULI_VERSION=1.0.0-beta9 DEPENDENCIES="henrikbjorn/phpspec-code-coverage:^2.0.2"
+          php: 7.1
+          # Disable code coverage until https://github.com/leanphp/phpspec-code-coverage/pull/38 is released
+          # DEPENDENCIES="leanphp/phpspec-code-coverage:^4.2" TEST_COMMAND="composer test-ci"
+          env: COMPOSER_FLAGS="--prefer-stable --prefer-lowest" COVERAGE=true TEST_COMMAND="composer test" PULI_VERSION=1.0.0-beta9
         - name: PHPUnit tests
-          php: 7.2
+          php: 7.3
           env: TEST_COMMAND="./vendor/bin/phpunit" DEPENDENCIES="phpunit/phpunit:^7.5 nyholm/psr7:^1.0 kriswallsmith/buzz:^1.0@beta php-http/curl-client:^1.0 php-http/message"
         - name: PHPUnit test with nothing installed
-          php: 7.2
+          php: 7.3
           env: TEST_COMMAND="./vendor/bin/phpunit --group=NothingInstalled" DEPENDENCIES="phpunit/phpunit:^7.5"
 
 before_install:
diff --git a/composer.json b/composer.json
index e6b6414..7a8e424 100644
--- a/composer.json
+++ b/composer.json
@@ -11,13 +11,14 @@
         }
     ],
     "require": {
-        "php": "^5.5 || ^7.0"
+        "php": "^7.1"
     },
     "require-dev": {
         "php-http/httplug": "^1.0 || ^2.0",
         "php-http/message-factory": "^1.0",
         "puli/composer-plugin": "1.0.0-beta10",
-        "phpspec/phpspec": "^2.4"
+        "phpspec/phpspec": "^5.1",
+        "akeneo/phpspec-skip-example-extension": "^4.0"
     },
     "suggest": {
         "puli/composer-plugin": "Sets up Puli which is recommended for Discovery to work. Check http://docs.php-http.org/en/latest/discovery.html for more details.",
@@ -39,7 +40,7 @@
     },
     "extra": {
         "branch-alias": {
-            "dev-master": "1.5-dev"
+            "dev-master": "1.7-dev"
         }
     },
     "conflict": {
diff --git a/phpspec.ci.yml b/phpspec.ci.yml
index fc7033d..1cc37e3 100644
--- a/phpspec.ci.yml
+++ b/phpspec.ci.yml
@@ -5,7 +5,8 @@ suites:
 formatter.name: pretty
 bootstrap: spec/autoload.php
 extensions:
-    - PhpSpec\Extension\CodeCoverageExtension
+    LeanPHP\PhpSpec\CodeCoverage\CodeCoverageExtension: ~
+    Akeneo\SkipExampleExtension: ~
 code_coverage:
     format: clover
     output: build/coverage.xml
diff --git a/phpspec.yml.dist b/phpspec.yml.dist
index 65d218e..2707b63 100644
--- a/phpspec.yml.dist
+++ b/phpspec.yml.dist
@@ -4,3 +4,5 @@ suites:
         psr4_prefix: Http\Discovery
 formatter.name: pretty
 bootstrap: spec/autoload.php
+extensions:
+    Akeneo\SkipExampleExtension: ~
diff --git a/spec/Strategy/PuliSpec.php b/spec/Strategy/PuliSpec.php
index 4be65f9..f3765a2 100644
--- a/spec/Strategy/PuliSpec.php
+++ b/spec/Strategy/PuliSpec.php
@@ -11,6 +11,9 @@
 use Puli\Repository\Api\ResourceRepository;
 use PhpSpec\ObjectBehavior;
 
+/**
+ * @require \NotPHP73
+ */
 class PuliSpec extends ObjectBehavior
 {
     function let(
@@ -67,7 +70,7 @@ function it_returns_a_class_binding_with_dependency(
     }
 
 
-    public function getMatchers()
+    public function getMatchers(): array
     {
         return [
             'haveCandidate' => function ($subject, $class, $condition) {
diff --git a/spec/autoload.php b/spec/autoload.php
index 1f0ffd1..3b1228e 100644
--- a/spec/autoload.php
+++ b/spec/autoload.php
@@ -7,3 +7,9 @@
         'Puli\\GeneratedPuliFactory' => __DIR__.'/../.puli/GeneratedPuliFactory.php',
     ]);
 }
+
+if (PHP_VERSION_ID >= 70300 && PHP_VERSION_ID < 70400) {
+    class PHP73 {}
+} else {
+    class NotPHP73 {}
+}