diff --git a/src/Asset/CssOptimizer.php b/src/Asset/CssOptimizer.php
index 494e9af..0d278e3 100644
--- a/src/Asset/CssOptimizer.php
+++ b/src/Asset/CssOptimizer.php
@@ -109,7 +109,7 @@ class CssOptimizer extends AssetOptimizer {
    * @return string
    *   The updated contents.
    */
-  protected function updateUrls($contents, $path) {
+  public function updateUrls($contents, $path) {
     // Determine the file's directory.
     $directory = '/' . dirname($path);
 
@@ -119,6 +119,8 @@ class CssOptimizer extends AssetOptimizer {
 
     // Alter all internal url() paths. Leave external paths alone. We don't need
     // to normalize absolute paths here because that will be done later.
+    // Expected form: url("/images/file.jpg") which gets converted to
+    // url("${directory}/images/file.jpg").
     return preg_replace('/url\(\s*([\'"]?)(?![a-z]+:|\/+)([^\'")]+)([\'"]?)\s*\)/i', 'url(\1' . $directory . '\2\3)', $contents);
   }
 
diff --git a/tests/src/Kernel/Asset/CssOptimizerUnitTest.php b/tests/src/Kernel/Asset/CssOptimizerUnitTest.php
new file mode 100644
index 0000000..c52474a
--- /dev/null
+++ b/tests/src/Kernel/Asset/CssOptimizerUnitTest.php
@@ -0,0 +1,83 @@
+<?php
+
+namespace Drupal\Tests\advagg\Kernel\Asset;
+
+use Drupal\KernelTests\KernelTestBase;
+
+/**
+ * Tests the CSS asset optimizer.
+ *
+ * @group advagg
+ */
+class CssOptimizerUnitTest extends KernelTestBase {
+
+  /**
+   * Modules to enable.
+   *
+   * @var array
+   */
+  public static $modules = ['advagg'];
+
+  /**
+   * The Optimizer.
+   *
+   * @var \Drupal\advagg\Asset\CssOptimizer
+   */
+  protected $optimizer;
+
+  /**
+   * The directory for comparison/getting CSS files from.
+   *
+   * @var string
+   */
+  protected $dir;
+
+  /**
+   * {@inheritdoc}
+   */
+  protected function setUp() {
+    parent::setUp();
+    $this->installConfig('advagg');
+    $this->optimizer = \Drupal::service('advagg.optimizer.css');
+    $this->dir = base_path() . 'modules/contrib/advagg/tests/src/Kernel/Asset/';
+  }
+
+  /**
+   * Provides data for the url update test.
+   */
+  public function providerTestUrlUpdate() {
+    return [
+      [
+        'url_test_same_dir.css',
+        $this->dir . 'css_test_files/icon-foo.svg',
+      ],
+      [
+        'url_test_child_dir.css',
+        $this->dir . 'css_test_files/images/icon-foo.svg',
+      ],
+      [
+        'url_test_parent_dir.css',
+        $this->dir . 'css_test_files/../images/icon-foo.svg',
+      ],
+    ];
+  }
+
+  /**
+   * Tests the urlUpdate() method.
+   *
+   * @param string $file
+   *   The file to test.
+   * @param string $expected
+   *   The expected url string.
+   *
+   * @dataProvider providerTestUrlUpdate
+   */
+  public function testUrlUpdate($file, $expected) {
+    $path = $this->dir . 'css_test_files/' . $file;
+    $absolute_path = dirname(__FIlE__) . '/css_test_files/';
+    $contents = file_get_contents($absolute_path . $file);
+    $replaced_urls = $this->optimizer->updateUrls($contents, $path);
+    $this->assertTrue(strstr($replaced_urls, $expected));
+  }
+
+}
diff --git a/tests/src/Kernel/Asset/css_test_files/url_test_child_dir.css b/tests/src/Kernel/Asset/css_test_files/url_test_child_dir.css
new file mode 100644
index 0000000..8a91715
--- /dev/null
+++ b/tests/src/Kernel/Asset/css_test_files/url_test_child_dir.css
@@ -0,0 +1,3 @@
+.icon-foo {
+    background-image: url("images/icon-foo.svg");
+}
diff --git a/tests/src/Kernel/Asset/css_test_files/url_test_parent_dir.css b/tests/src/Kernel/Asset/css_test_files/url_test_parent_dir.css
new file mode 100644
index 0000000..acd77cc
--- /dev/null
+++ b/tests/src/Kernel/Asset/css_test_files/url_test_parent_dir.css
@@ -0,0 +1,3 @@
+.icon-foo {
+    background-image: url("../images/icon-foo.svg");
+}
diff --git a/tests/src/Kernel/Asset/css_test_files/url_test_same_dir.css b/tests/src/Kernel/Asset/css_test_files/url_test_same_dir.css
new file mode 100644
index 0000000..0a88f0c
--- /dev/null
+++ b/tests/src/Kernel/Asset/css_test_files/url_test_same_dir.css
@@ -0,0 +1,3 @@
+.icon-foo {
+    background-image: url("icon-foo.svg");
+}