diff --git a/test/PHPMailer/DKIMTest.php b/test/PHPMailer/DKIMTest.php
index 48080460..63034ab0 100644
--- a/test/PHPMailer/DKIMTest.php
+++ b/test/PHPMailer/DKIMTest.php
@@ -13,7 +13,7 @@
 
 namespace PHPMailer\Test\PHPMailer;
 
-use Exception;
+use PHPMailer\PHPMailer\Exception;
 use PHPMailer\PHPMailer\PHPMailer;
 use PHPMailer\Test\SendTestCase;
 
@@ -240,21 +240,6 @@ final class DKIMTest extends SendTestCase
         self::assertTrue($this->Mail->send(), 'DKIM signed mail via mail() failed');
     }
 
-    /**
-     * Verify behaviour of the DKIM_Sign method when Open SSL is not available.
-     *
-     * @covers \PHPMailer\PHPMailer\PHPMailer::DKIM_Sign
-     */
-    public function testDKIMSignOpenSSLNotAvailable()
-    {
-        if (extension_loaded('openssl')) {
-            $this->markTestSkipped('Test requires OpenSSL *not* to be available');
-        }
-
-        $signature = $this->Mail->DKIM_Sign('foo');
-        self::assertSame('', $signature);
-    }
-
     /**
      * Verify behaviour of the DKIM_Sign method when Open SSL is not available and exceptions is enabled.
      *
diff --git a/test/PHPMailer/DKIMWithoutExceptionsTest.php b/test/PHPMailer/DKIMWithoutExceptionsTest.php
new file mode 100644
index 00000000..6e8429bb
--- /dev/null
+++ b/test/PHPMailer/DKIMWithoutExceptionsTest.php
@@ -0,0 +1,47 @@
+<?php
+
+/**
+ * PHPMailer - PHP email transport unit tests.
+ * PHP version 5.5.
+ *
+ * @author    Marcus Bointon <phpmailer@synchromedia.co.uk>
+ * @author    Andy Prevost
+ * @copyright 2012 - 2020 Marcus Bointon
+ * @copyright 2004 - 2009 Andy Prevost
+ * @license   https://www.gnu.org/licenses/old-licenses/lgpl-2.1.html GNU Lesser General Public License
+ */
+
+namespace PHPMailer\Test\PHPMailer;
+
+use PHPMailer\PHPMailer\PHPMailer;
+use PHPMailer\Test\TestCase;
+
+/**
+ * Test DKIM signing functionality.
+ *
+ * @group dkim
+ */
+final class DKIMWithoutExceptionsTest extends TestCase
+{
+    /**
+     * Whether or not to initialize the PHPMailer object to throw exceptions.
+     *
+     * @var bool|null
+     */
+    const USE_EXCEPTIONS = false;
+
+    /**
+     * Verify behaviour of the DKIM_Sign method when Open SSL is not available and exceptions is disabled.
+     *
+     * @covers \PHPMailer\PHPMailer\PHPMailer::DKIM_Sign
+     */
+    public function testDKIMSignOpenSSLNotAvailable()
+    {
+        if (extension_loaded('openssl')) {
+            $this->markTestSkipped('Test requires OpenSSL *not* to be available');
+        }
+
+        $signature = $this->Mail->DKIM_Sign('foo');
+        self::assertSame('', $signature);
+    }
+}