diff --git a/core/lib/Drupal/Component/Annotation/composer.json b/core/lib/Drupal/Component/Annotation/composer.json
index 76254ea..ff33d29 100644
--- a/core/lib/Drupal/Component/Annotation/composer.json
+++ b/core/lib/Drupal/Component/Annotation/composer.json
@@ -8,9 +8,9 @@
     "php": ">=5.5.9",
     "doctrine/common": "2.5.*",
     "doctrine/annotations": "1.2.*",
-    "drupal/core-fileCache": "~8.2",
-    "drupal/core-plugin": "~8.2",
-    "drupal/core-utility": "~8.2"
+    "drupal/core-fileCache": "^8.2",
+    "drupal/core-plugin": "^8.2",
+    "drupal/core-utility": "^8.2"
   },
   "autoload": {
     "psr-4": {
diff --git a/core/lib/Drupal/Component/Bridge/composer.json b/core/lib/Drupal/Component/Bridge/composer.json
index af6da18..928d867 100644
--- a/core/lib/Drupal/Component/Bridge/composer.json
+++ b/core/lib/Drupal/Component/Bridge/composer.json
@@ -6,7 +6,7 @@
   "license": "GPL-2.0+",
   "require": {
     "php": ">=5.5.9",
-    "zendframework/zend-feed": "~2.4"
+    "zendframework/zend-feed": "^2.4"
   },
   "autoload": {
     "psr-4": {
diff --git a/core/lib/Drupal/Component/Datetime/composer.json b/core/lib/Drupal/Component/Datetime/composer.json
index 04d9653..1df4328 100644
--- a/core/lib/Drupal/Component/Datetime/composer.json
+++ b/core/lib/Drupal/Component/Datetime/composer.json
@@ -6,7 +6,7 @@
   "license": "GPL-2.0+",
   "require": {
     "php": ">=5.5.9",
-    "drupal/core-utility": "~8.2"
+    "drupal/core-utility": "^8.2"
   },
   "autoload": {
     "psr-4": {
diff --git a/core/lib/Drupal/Component/DependencyInjection/composer.json b/core/lib/Drupal/Component/DependencyInjection/composer.json
index 7701313..cf25192 100644
--- a/core/lib/Drupal/Component/DependencyInjection/composer.json
+++ b/core/lib/Drupal/Component/DependencyInjection/composer.json
@@ -12,7 +12,7 @@
   },
   "require": {
     "php": ">=5.5.9",
-    "symfony/dependency-injection": "~2.8"
+    "symfony/dependency-injection": "^2.8"
   },
   "suggest": {
     "symfony/expression-language": "For using expressions in service container configuration"
diff --git a/core/lib/Drupal/Component/Diff/composer.json b/core/lib/Drupal/Component/Diff/composer.json
index 0d7f3d3..cc58453 100644
--- a/core/lib/Drupal/Component/Diff/composer.json
+++ b/core/lib/Drupal/Component/Diff/composer.json
@@ -6,7 +6,7 @@
   "license": "GPL-2.0+",
   "require": {
     "php": ">=5.5.9",
-    "drupal/utility": "~8.2"
+    "drupal/utility": "^8.2"
   },
   "autoload": {
     "psr-4": {
diff --git a/core/lib/Drupal/Component/Discovery/composer.json b/core/lib/Drupal/Component/Discovery/composer.json
index 1b0acb6..588480e 100644
--- a/core/lib/Drupal/Component/Discovery/composer.json
+++ b/core/lib/Drupal/Component/Discovery/composer.json
@@ -6,8 +6,8 @@
   "license": "GPL-2.0+",
   "require": {
     "php": ">=5.5.9",
-    "drupal/core-filecache": "~8.2",
-    "drupal/core-serialization": "~8.2"
+    "drupal/core-filecache": "^8.2",
+    "drupal/core-serialization": "^8.2"
   },
   "autoload": {
     "psr-4": {
diff --git a/core/lib/Drupal/Component/EventDispatcher/composer.json b/core/lib/Drupal/Component/EventDispatcher/composer.json
index be66232..a4db6fa 100644
--- a/core/lib/Drupal/Component/EventDispatcher/composer.json
+++ b/core/lib/Drupal/Component/EventDispatcher/composer.json
@@ -6,8 +6,8 @@
   "license": "GPL-2.0+",
   "require": {
     "php": ">=5.5.9",
-    "symfony/dependency-injection": "~2.8",
-    "symfony/event-dispatcher": "~2.7"
+    "symfony/dependency-injection": "^2.8",
+    "symfony/event-dispatcher": "^2.7"
   },
   "autoload": {
     "psr-4": {
diff --git a/core/lib/Drupal/Component/Gettext/composer.json b/core/lib/Drupal/Component/Gettext/composer.json
index 2dab698..1651234 100644
--- a/core/lib/Drupal/Component/Gettext/composer.json
+++ b/core/lib/Drupal/Component/Gettext/composer.json
@@ -10,7 +10,7 @@
   },
   "require": {
     "php": ">=5.5.9",
-    "drupal/core-utility": "~8.2"
+    "drupal/core-utility": "^8.2"
   },
   "autoload": {
     "psr-4": {
diff --git a/core/lib/Drupal/Component/HttpFoundation/composer.json b/core/lib/Drupal/Component/HttpFoundation/composer.json
index 1b3920b..b86ab16 100644
--- a/core/lib/Drupal/Component/HttpFoundation/composer.json
+++ b/core/lib/Drupal/Component/HttpFoundation/composer.json
@@ -6,7 +6,7 @@
   "license": "GPL-2.0+",
   "require": {
     "php": ">=5.5.9",
-    "symfony/http-foundation": "~2.7"
+    "symfony/http-foundation": "^2.7"
   },
   "autoload": {
     "psr-4": {
diff --git a/core/lib/Drupal/Component/Plugin/composer.json b/core/lib/Drupal/Component/Plugin/composer.json
index 4ffeeed..1182657 100644
--- a/core/lib/Drupal/Component/Plugin/composer.json
+++ b/core/lib/Drupal/Component/Plugin/composer.json
@@ -6,7 +6,7 @@
   "license": "GPL-2.0+",
   "require": {
     "php": ">=5.5.9",
-    "symfony/validator": "~2.7"
+    "symfony/validator": "^2.7"
   },
   "autoload": {
     "psr-4": {
diff --git a/core/lib/Drupal/Component/Render/composer.json b/core/lib/Drupal/Component/Render/composer.json
index 88291e9..50c2f70 100644
--- a/core/lib/Drupal/Component/Render/composer.json
+++ b/core/lib/Drupal/Component/Render/composer.json
@@ -6,7 +6,7 @@
   "license": "GPL-2.0+",
   "require": {
     "php": ">=5.5.9",
-    "drupal/core-utility": "~8.2"
+    "drupal/core-utility": "^8.2"
   },
   "autoload": {
     "psr-4": {
diff --git a/core/lib/Drupal/Component/Serialization/composer.json b/core/lib/Drupal/Component/Serialization/composer.json
index 5d629cf..97fd639 100644
--- a/core/lib/Drupal/Component/Serialization/composer.json
+++ b/core/lib/Drupal/Component/Serialization/composer.json
@@ -6,7 +6,7 @@
   "license": "GPL-2.0+",
   "require": {
     "php": ">=5.5.9",
-    "symfony/yaml": "~2.7"
+    "symfony/yaml": "^2.7"
   },
   "autoload": {
     "psr-4": {
diff --git a/core/lib/Drupal/Component/Utility/composer.json b/core/lib/Drupal/Component/Utility/composer.json
index 13671ef..5fa2079 100644
--- a/core/lib/Drupal/Component/Utility/composer.json
+++ b/core/lib/Drupal/Component/Utility/composer.json
@@ -7,7 +7,7 @@
   "require": {
     "php": ">=5.5.9",
     "paragonie/random_compat": "^1.0|^2.0",
-    "drupal/core-render": "~8.2"
+    "drupal/core-render": "^8.2"
   },
   "autoload": {
     "psr-4": {
diff --git a/core/lib/Drupal/Component/Uuid/composer.json b/core/lib/Drupal/Component/Uuid/composer.json
index deca54b..7c43422 100644
--- a/core/lib/Drupal/Component/Uuid/composer.json
+++ b/core/lib/Drupal/Component/Uuid/composer.json
@@ -10,7 +10,7 @@
   },
   "require": {
     "php": ">=5.5.9",
-    "drupal/core-utility": "~8.2"
+    "drupal/core-utility": "^8.2"
   },
   "autoload": {
     "psr-4": {
diff --git a/core/tests/Drupal/Tests/ComposerIntegrationTest.php b/core/tests/Drupal/Tests/ComposerIntegrationTest.php
index a64804c..5619b84 100644
--- a/core/tests/Drupal/Tests/ComposerIntegrationTest.php
+++ b/core/tests/Drupal/Tests/ComposerIntegrationTest.php
@@ -89,6 +89,46 @@ public function testComposerLockHash() {
   }
 
   /**
+   * Tests composer.json versions.
+   *
+   * @param string $path
+   *   Path to a composer.json to test.
+   *
+   * @dataProvider providerTestComposerJson
+   */
+  public function testComposerTilde($path) {
+    $content = json_decode(file_get_contents($path), TRUE);
+    $composer_keys = array_intersect(['require', 'require-dev'], array_keys($content));
+    if (empty($composer_keys)) {
+      $this->markTestSkipped("$path has no keys to test");
+    }
+    foreach ($composer_keys as $composer_key) {
+      foreach ($content[$composer_key] as $dependency => $version) {
+        $this->assertFalse(strpos($version, '~'), "Dependency $dependency in $path contains a tilde, use a caret.");
+      }
+    }
+  }
+
+  /**
+   * Data provider for all the composer.json provided by Drupal core.
+   *
+   * @return array
+   */
+  public function providerTestComposerJson() {
+    $root = realpath(__DIR__ . '/../../../../');
+    $tests = [[$root . '/composer.json']];
+    $directory = new \RecursiveDirectoryIterator($root . '/core');
+    $iterator = new \RecursiveIteratorIterator($directory);
+    /** @var \SplFileInfo $file */
+    foreach ($iterator as $file) {
+      if ($file->getFilename() === 'composer.json' && strpos($file->getPath(), 'core/modules/system/tests/fixtures/HtaccessTest') === FALSE) {
+        $tests[] = [$file->getRealPath()];
+      }
+    }
+    return $tests;
+  }
+
+  /**
    * Tests core's composer.json replace section.
    *
    * Verify that all core modules are also listed in the 'replace' section of