diff --git a/README.rst b/README.rst
index 200c97ce45f..b8dc3271c81 100644
--- a/README.rst
+++ b/README.rst
@@ -423,7 +423,8 @@ Choose from the list of available rules:
 
 * **constant_case** [@PSR2, @Symfony, @PhpCsFixer]
 
-  The PHP constants ``true``, ``false``, and ``null`` MUST be in lower case.
+  The PHP constants ``true``, ``false``, and ``null`` MUST be written using the
+  correct casing.
 
   Configuration options:
 
diff --git a/src/Fixer/Casing/ConstantCaseFixer.php b/src/Fixer/Casing/ConstantCaseFixer.php
index 98b57829700..c476269b595 100644
--- a/src/Fixer/Casing/ConstantCaseFixer.php
+++ b/src/Fixer/Casing/ConstantCaseFixer.php
@@ -23,9 +23,9 @@
 use PhpCsFixer\Tokenizer\Tokens;
 
 /**
- * Fixer for rules defined in PSR2 ¶2.5.
+ * Fixer for constants case.
  *
- * @author Dariusz Rumiński <dariusz.ruminski@gmail.com>
+ * @author Pol Dellaiera <pol.dellaiera@protonmail.com>
  */
 final class ConstantCaseFixer extends AbstractFixer implements ConfigurationDefinitionFixerInterface
 {
@@ -44,11 +44,15 @@ public function configure(array $configuration = null)
         parent::configure($configuration);
 
         if ('lower' === $this->configuration['case']) {
-            $this->fixFunction = 'strtolower';
+            $this->fixFunction = static function ($token) {
+                return strtolower($token);
+            };
         }
 
         if ('upper' === $this->configuration['case']) {
-            $this->fixFunction = 'strtoupper';
+            $this->fixFunction = static function ($token) {
+                return strtoupper($token);
+            };
         }
     }
 
@@ -58,7 +62,7 @@ public function configure(array $configuration = null)
     public function getDefinition()
     {
         return new FixerDefinition(
-            'The PHP constants `true`, `false`, and `null` MUST be in lower case.',
+            'The PHP constants `true`, `false`, and `null` MUST be written using the correct casing.',
             [new CodeSample("<?php\n\$a = FALSE;\n\$b = True;\n\$c = nuLL;\n")]
         );
     }