diff --git a/composer.json b/composer.json
index 26112441e..fad627e48 100644
--- a/composer.json
+++ b/composer.json
@@ -10,8 +10,8 @@
         }
     ],
     "require": {
-        "php": ">=5.5",
-        "nikic/PHP-Parser": ">=3.0.2"
+        "php": "^5.5 || ^7.0",
+        "nikic/PHP-Parser": "^3.0.2"
     },
     "bin": ["bin/psalm"],
     "autoload": {
@@ -25,7 +25,7 @@
         }
     },
     "require-dev": {
-        "phpunit/phpunit": ">=5.7.4",
+        "phpunit/phpunit": "^5.7.4",
         "squizlabs/php_codesniffer": "^2.7"
     },
     "scripts": {