diff --git a/.travis.yml b/.travis.yml
index 65bd6ba..ff444b7 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -18,16 +18,16 @@ matrix:
            CHECK_MBSTRING=1
     - dist: precise
       php: "5.6"
-      env: USE_PSALM=1
+      env: USE_PSALM=0
            CHECK_MBSTRING=1
     - php: "7.0"
-      env: USE_PSALM=1
+      env: USE_PSALM=0
            CHECK_MBSTRING=1
     - php: "7.1"
-      env: USE_PSALM=1
-           CHECK_MBSTRING=1
+      env: USE_PSALM=0
+           CHECK_MBSTRING=0
     - php: "7.2"
-      env: USE_PSALM=1
+      env: USE_PSALM=0
            CHECK_MBSTRING=0
     - php: "7.3"
       env: USE_PSALM=1
@@ -36,7 +36,7 @@ matrix:
       env: USE_PSALM=1
            CHECK_MBSTRING=0
     - php: "nightly"
-      env: USE_PSALM=1
+      env: USE_PSALM=0
            CHECK_MBSTRING=0
     - php: "hhvm"
       env: USE_PSALM=1
@@ -45,15 +45,18 @@ matrix:
       env: USE_PSALM=1
            CHECK_MBSTRING=0
   allow_failures:
+    - php: "nightly"
     - php: "hhvm"
     - php: "master"
 
 install:
-    - composer self-update
-    - composer install
-    - if [[ $USE_PSALM -eq 1 ]]; then composer require --dev "vimeo/psalm:^0|^1|^2"; fi
+    - travis_retry composer install
+    - if [[ $USE_PSALM -eq 1 ]]; then composer require --dev "phpunit/phpunit:>=4"; fi
+    - if [[ $USE_PSALM -eq 1 ]]; then rm composer.lock; fi
+    - if [[ $USE_PSALM -eq 1 ]]; then rm -rf vendor; fi
+    - if [[ $USE_PSALM -eq 1 ]]; then composer require --dev "vimeo/psalm:^3"; fi
 
 script:
     - vendor/bin/phpunit
-    - php -dmbstring.func_overload=7 vendor/bin/phpunit
+    - if [[ $CHECK_MBSTRING -eq 1 ]]; then php -dmbstring.func_overload=7 vendor/bin/phpunit; fi
     - if [[ $USE_PSALM -eq 1 ]]; then vendor/bin/psalm; fi
diff --git a/other/phpunit-shim.php b/other/phpunit-shim.php
new file mode 100644
index 0000000..3c5d0e2
--- /dev/null
+++ b/other/phpunit-shim.php
@@ -0,0 +1,6 @@
+<?php
+
+class PHPUnit_Framework_TestCase extends \PHPUnit\Framework\TestCase
+{
+
+}
diff --git a/phpunit-autoload.php b/phpunit-autoload.php
new file mode 100644
index 0000000..87b01aa
--- /dev/null
+++ b/phpunit-autoload.php
@@ -0,0 +1,14 @@
+<?php
+
+require_once __DIR__ . '/psalm-autoload.php';
+
+/**
+ * This is necessary for PHPUnit on PHP >= 5.3
+ *
+ * Class PHPUnit_Framework_TestCase
+ */
+if (PHP_VERSION_ID >= 50300) {
+    if (!class_exists('PHPUnit_Framework_TestCase')) {
+        require_once __DIR__ . '/other/phpunit-shim.php';
+    }
+}
diff --git a/phpunit.xml.dist b/phpunit.xml.dist
index 19c5e22..4887008 100644
--- a/phpunit.xml.dist
+++ b/phpunit.xml.dist
@@ -1,31 +1,13 @@
 <?xml version="1.0" encoding="UTF-8"?>
-<phpunit backupGlobals="true"
-         backupStaticAttributes="false"
-         bootstrap="lib/random.php"
-         colors="true"
-         convertErrorsToExceptions="true"
-         convertNoticesToExceptions="true"
-         convertWarningsToExceptions="true"
-         failOnRisky="true"
-         failOnWarning="true"
-         processIsolation="false"
-         stopOnError="false"
-         stopOnFailure="false"
-         syntaxCheck="true"
->
-    <testsuites>
-        <testsuite name="Unit">
-            <directory>tests/unit</directory>
-        </testsuite>
-    </testsuites>
-    <testsuites>
-        <testsuite name="Random Compat Test Suite">
-            <directory suffix="Test.php">./tests/unit</directory>
-        </testsuite>
-    </testsuites>
-    <filter>
-        <whitelist processUncoveredFilesFromWhitelist="true">
-            <directory suffix=".php">./lib</directory>
-        </whitelist>
-    </filter>
+<phpunit xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" backupGlobals="true" backupStaticAttributes="false" bootstrap="phpunit-autoload.php" colors="true" convertErrorsToExceptions="true" convertNoticesToExceptions="true" convertWarningsToExceptions="true" failOnRisky="true" failOnWarning="true" processIsolation="false" stopOnError="false" stopOnFailure="false" xsi:noNamespaceSchemaLocation="https://schema.phpunit.de/9.3/phpunit.xsd">
+  <coverage processUncoveredFiles="true">
+    <include>
+      <directory suffix=".php">./lib</directory>
+    </include>
+  </coverage>
+  <testsuites>
+    <testsuite name="Random Compat Test Suite">
+      <directory suffix="Test.php">./tests/unit</directory>
+    </testsuite>
+  </testsuites>
 </phpunit>
diff --git a/psalm-autoload.php b/psalm-autoload.php
index d71d1b8..fb0c89a 100644
--- a/psalm-autoload.php
+++ b/psalm-autoload.php
@@ -1,9 +1,9 @@
 <?php
 
-require_once 'lib/byte_safe_strings.php';
-require_once 'lib/cast_to_int.php';
-require_once 'lib/error_polyfill.php';
-require_once 'other/ide_stubs/libsodium.php';
-require_once 'lib/random.php';
+require_once __DIR__ . '/lib/byte_safe_strings.php';
+require_once __DIR__ . '/lib/cast_to_int.php';
+require_once __DIR__ . '/lib/error_polyfill.php';
+require_once __DIR__ . '/other/ide_stubs/libsodium.php';
+require_once __DIR__ . '/lib/random.php';
 
 $int = random_int(0, 65536);
diff --git a/psalm.xml b/psalm.xml
index d48076a..719cb7f 100644
--- a/psalm.xml
+++ b/psalm.xml
@@ -1,28 +1,36 @@
 <?xml version="1.0"?>
 <psalm
-    autoloader="psalm-autoload.php"
-    useDocblockTypes="true"
-    totallyTyped="true"
+        autoloader="psalm-autoload.php"
+        useDocblockTypes="true"
+        totallyTyped="true"
 >
     <projectFiles>
         <directory name="lib" />
     </projectFiles>
     <issueHandlers>
+        <ReferenceConstraintViolation errorLevel="info" />
+        <!-- Type strictness surrounding /dev/urandom reads -->
         <RedundantConditionGivenDocblockType errorLevel="info" />
-            <!-- We have to be explicit because PHP 5 lacks scalar types -->
+        <!-- We have to be explicit because PHP 5 lacks scalar types -->
+        <DocblockTypeContradiction errorLevel="info" />
+        <!-- We're strict about runtime checks -->
+        <DuplicateFunction errorLevel="info" />
+        <!-- We're a polyfill library! -->
         <UnresolvableInclude errorLevel="info" />
-            <!-- Because we put the variants into their own subdirectory -->
+        <!-- Because we put the variants into their own subdirectory -->
         <DuplicateClass errorLevel="info" />
-            <!-- Later versions of Psalm are only PHP 7 compatible, which
-                 sees our redefinition of Error and TypeError as duplicate
-                 class errors. -->
+        <!-- Later versions of Psalm are only PHP 7 compatible, which
+             sees our redefinition of Error and TypeError as duplicate
+             class errors. -->
+        <UndefinedDocblockClass errorLevel="info" />
+        <!-- COM is Windows only -->
         <UndefinedConstant errorLevel="info" />
-            <!-- The Mcrypt constants aren't defined in PHP 7.2 -->
+        <!-- The Mcrypt constants aren't defined in PHP 7.2 -->
         <MissingReturnType errorLevel="info" />
-            <!-- False positive with some versions of (Psalm, PHP) -->
+        <!-- False positive with some versions of (Psalm, PHP) -->
         <InvalidReturnType errorLevel="info" />
-            <!-- The "last resort" function in lib/random.php -->
+        <!-- The "last resort" function in lib/random.php -->
         <MixedInferredReturnType errorLevel="suppress" />
-            <!-- Only used in totallyTyped mode -->
+        <!-- Only used in totallyTyped mode -->
     </issueHandlers>
 </psalm>