diff --git a/tests/src/Behat/OeThemeTestContext.php b/tests/src/Behat/OeThemeTestContext.php
index c2286b74f7..ddaa59b41d 100644
--- a/tests/src/Behat/OeThemeTestContext.php
+++ b/tests/src/Behat/OeThemeTestContext.php
@@ -436,7 +436,13 @@ public function iShouldSeeTheSiteHeader(string $ecl_branding): void {
     $this->assertSession()->elementExists('css', 'a.ecl-site-header__logo-link .ecl-site-header__logo-image');
     $this->assertSession()->elementExists('css', '.ecl-site-header__top .ecl-site-header__action .ecl-site-header__language-selector');
     $this->assertSession()->elementExists('css', '.ecl-site-header__top .ecl-site-header__action .ecl-site-header__search-container');
-    $this->assertSession()->elementExists('css', '.ecl-site-header__banner');
+    $menu = $this->getSession()->getPage()->find('css', 'header.ecl-site-header .ecl-menu.ecl-menu--group1');
+    if ($ecl_branding === 'Core' && !$menu) {
+      $this->assertSession()->elementNotExists('css', '.ecl-site-header__banner');
+    }
+    else {
+      $this->assertSession()->elementExists('css', '.ecl-site-header__banner');
+    }
   }
 
   /**
diff --git a/tests/src/Functional/ConfigurationTest.php b/tests/src/Functional/ConfigurationTest.php
index 240abba207..e338c864c4 100755
--- a/tests/src/Functional/ConfigurationTest.php
+++ b/tests/src/Functional/ConfigurationTest.php
@@ -187,9 +187,9 @@ public function testChangeEclBranding(): void {
       $assert_session->elementExists('css', 'header.ecl-site-header div.ecl-site-header__top');
       $assert_session->elementExists('css', 'header.ecl-site-header div.ecl-site-header__top div.ecl-site-header__action');
 
-      // Make sure that 'Site name' banner is present in the site header
-      // for Core template.
-      $assert_session->elementExists('css', 'header.ecl-site-header .ecl-site-header__banner .ecl-container');
+      // Make sure that banner is not present in the site header for
+      // the Core template, if the site name and menu are not shown.
+      $assert_session->elementNotExists('css', 'header.ecl-site-header .ecl-site-header__banner .ecl-container');
 
       // Visit theme administration page.
       $this->drupalGet('/admin/appearance/settings/' . $active_theme);