diff -u b/core/includes/menu.inc b/core/includes/menu.inc
--- b/core/includes/menu.inc
+++ b/core/includes/menu.inc
@@ -2196,7 +2196,7 @@
  * @param $module
  *   The name of the implementing module. This is used to prefix the key for
  *   each contextual link, which is transformed into a CSS class during
- *   rendering by links.html.twig. For example, if $module is 'block' and the
+ *   rendering by theme_links(). For example, if $module is 'block' and the
  *   retrieved local task path argument is 'edit', then the resulting CSS class
  *   will be 'block-edit'.
  * @param $parent_path
@@ -2204,7 +2204,7 @@
  * @param $module
  *   The name of the implementing module. This is used to prefix the key for
  *   each contextual link, which is transformed into a CSS class during
- *   rendering by theme_links(). For example, if $module is 'block' and the
+ *   rendering by links.html.twig. For example, if $module is 'block' and the
  *   retrieved local task path argument is 'edit', then the resulting CSS class
  *   will be 'block-edit'.
  * @param $parent_path
diff -u b/core/includes/theme.inc b/core/includes/theme.inc
--- b/core/includes/theme.inc
+++ b/core/includes/theme.inc
@@ -1615,15 +1615,14 @@
  *     associative array or a string. If it's an array, it can have the
  *     following elements:
  *     - text: The heading text.
- *     - level: The heading level (e.g. 'h2', 'h3').
  *     - class: (optional) An array of the CSS classes for the heading.
- *     When using a string it will be used as the text of the heading and the
- *     level will default to 'h2'. Headings should be used on navigation menus
- *     and any list of links that consistently appears on multiple pages. To
- *     make the heading invisible use the 'visually-hidden' CSS class. Do not
- *     use 'display:none', which removes it from screen-readers and assistive
- *     technology. Headings allow screen-reader and keyboard only users to
- *     navigate to or skip the links. See
+ *     When using a string it will be used as the text of the heading.
+ *     Headings should be used on navigation menus and any list of links that
+ *     consistently appears on multiple pages. To make the heading invisible
+ *     use the 'visually-hidden' CSS class. Do not use 'display:none', which
+ *     removes it from screen-readers and assistive technology. Headings allow
+ *     screen-reader and keyboard only users to navigate to or skip the links.
+ *     See
  *     http://juicystudio.com/article/screen-readers-display-none.php and
  *     http://www.w3.org/TR/WCAG-TECHS/H42.html for more information.
  */
@@ -1635,7 +1634,7 @@
   if (!empty($links)) {
     // Prepend the heading to the list, if any.
     if (!empty($heading)) {
-      // Convert a string heading into an array, using a H2 tag by default.
+      // Convert a string heading into an array.
       if (is_string($heading)) {
         $heading = array('text' => $heading);
       }
reverted:
--- b/core/modules/system/templates/links.html.twig
+++ /dev/null
@@ -1,62 +0,0 @@
-{#
-/**
- * @file
- * Default theme implementation for a set of links.
- *
- * Available variables:
- * - attributes: Attributes for the UL containing the list of links.
- * - links: Links to be output.
- *   Each link will have the following elements:
- *   - title: The link text.
- *   - href: The link URL. If omitted, the 'title' is shown as a plain text
- *     item in the links list. If 'href' is supplied, the entire link is passed
- *     to l() as its $options parameter.
- *   - html: (optional) Whether or not 'title' is HTML. If set, the title will
- *     not be passed through check_plain().
- *   - attributes: (optional) HTML attributes for the anchor, or for the <span>
- *     tag if no 'href' is supplied.
- * - heading: (optional) A heading to precede the links. May be an associative
- *   array or a string.
- *   - text: The heading text.
- *   - level: The heading level (e.g. 'h2', 'h3').
- *   - attributes: (optional) A keyed list of attributes for the heading.
- *   If the heading is a string, it will be used as the text of the heading and
- *   the level will default to 'h2'.
- *
- *   Headings should be used on navigation menus and any list of links that
- *   consistently appears on multiple pages. To make the heading invisible use
- *   the 'visually-hidden' CSS class. Do not use 'display:none', which
- *   removes it from screen-readers and assistive technology. Headings allow
- *   screen-reader and keyboard only users to navigate to or skip the links.
- *   See http://juicystudio.com/article/screen-readers-display-none.php and
- *   http://www.w3.org/TR/WCAG-TECHS/H42.html for more information.
- *
- * @see template_preprocess_links()
- *
- * @ingroup themeable
- */
-#}
-{% spaceless %}
-  {% if links %}
-    {% if heading %}
-      {% if heading.level %}
-        <{{ heading.level }}{{ heading.attributes }}>{{ heading.text }}</{{ heading.level }}>
-      {% else %}
-        <h2{{ heading.attributes }}>{{ heading.text }}</h2>
-      {% endif %}
-    {% endif %}
-    <ul{{ attributes }}>
-      {% for item in links %}
-        <li{{ item.attributes }}>
-          {%- if item.link -%}
-            {{ item.link }}
-          {%- elseif item.text_attributes -%}
-            <span{{ item.text_attributes }}>{{ item.text }}</span>
-          {%- else -%}
-            {{ item.text }}
-          {%- endif -%}
-        </li>
-      {% endfor %}
-    </ul>
-  {% endif %}
-{% endspaceless %}
only in patch2:
unchanged:
--- a/core/modules/system/templates/links.html.twig
+++ b/core/modules/system/templates/links.html.twig
@@ -0,0 +1,56 @@
+{#
+/**
+ * @file
+ * Default theme implementation for a set of links.
+ *
+ * Available variables:
+ * - attributes: Attributes for the UL containing the list of links.
+ * - links: Links to be output.
+ *   Each link will have the following elements:
+ *   - title: The link text.
+ *   - href: The link URL. If omitted, the 'title' is shown as a plain text
+ *     item in the links list. If 'href' is supplied, the entire link is passed
+ *     to l() as its $options parameter.
+ *   - html: (optional) Whether or not 'title' is HTML. If set, the title will
+ *     not be passed through check_plain().
+ *   - attributes: (optional) HTML attributes for the anchor, or for the <span>
+ *     tag if no 'href' is supplied.
+ * - heading: (optional) A heading to precede the links. May be an associative
+ *   array or a string.
+ *   - text: The heading text.
+ *   - attributes: (optional) A keyed list of attributes for the heading.
+ *   If the heading is a string, it will be used as the text of the heading.
+ *
+ *   Headings should be used on navigation menus and any list of links that
+ *   consistently appears on multiple pages. To make the heading invisible use
+ *   the 'visually-hidden' CSS class. Do not use 'display:none', which
+ *   removes it from screen-readers and assistive technology. Headings allow
+ *   screen-reader and keyboard only users to navigate to or skip the links.
+ *   See http://juicystudio.com/article/screen-readers-display-none.php and
+ *   http://www.w3.org/TR/WCAG-TECHS/H42.html for more information.
+ *
+ * @see template_preprocess_links()
+ *
+ * @ingroup themeable
+ */
+#}
+{% spaceless %}
+  {% if links %}
+    {% if heading %}
+      <h2{{ heading.attributes }}>{{ heading.text }}</h2>
+    {% endif %}
+    <ul{{ attributes }}>
+      {% for item in links %}
+        <li{{ item.attributes }}>
+          {%- if item.link -%}
+            {{ item.link }}
+          {%- elseif item.text_attributes -%}
+            <span{{ item.text_attributes }}>{{ item.text }}</span>
+          {%- else -%}
+            {{ item.text }}
+          {%- endif -%}
+        </li>
+      {% endfor %}
+    </ul>
+  {% endif %}
+{% endspaceless %}