diff --git a/datasette/static/mobile-column-actions.js b/datasette/static/mobile-column-actions.js
index bad963bf..a386b1fc 100644
--- a/datasette/static/mobile-column-actions.js
+++ b/datasette/static/mobile-column-actions.js
@@ -5,9 +5,7 @@ var MOBILE_COLUMN_DIALOG_TITLE_ID = "mobile-column-actions-title";
 function mobileColumnHeaders(manager) {
   return Array.from(
     document.querySelectorAll(manager.selectors.tableHeaders),
-  ).filter(
-    (th) => th.dataset.column && th.querySelector(".dropdown-menu-icon"),
-  );
+  ).filter((th) => th.dataset.column && th.dataset.isLinkColumn !== "1");
 }
 
 function mobileColumnMetaText(th) {
diff --git a/datasette/templates/_table.html b/datasette/templates/_table.html
index a1329ba7..ba34b60f 100644
--- a/datasette/templates/_table.html
+++ b/datasette/templates/_table.html
@@ -6,7 +6,7 @@
         <thead>
             <tr>
                 {% for column in display_columns %}
-                    <th {% if column.description %}data-column-description="{{ column.description }}" {% endif %}class="col-{{ column.name|to_css_class }}" scope="col" data-column="{{ column.name }}" data-column-type="{{ column.type.lower() }}" data-column-not-null="{{ column.notnull }}" data-is-pk="{% if column.is_pk %}1{% else %}0{% endif %}">
+                    <th {% if column.description %}data-column-description="{{ column.description }}" {% endif %}class="col-{{ column.name|to_css_class }}" scope="col" data-column="{{ column.name }}" data-column-type="{{ column.type.lower() }}" data-column-not-null="{{ column.notnull }}" data-is-pk="{% if column.is_pk %}1{% else %}0{% endif %}"{% if column.is_special_link_column %} data-is-link-column="1"{% endif %}>
                         {% if not column.sortable %}
                             {{ column.name }}
                         {% else %}
diff --git a/datasette/views/table.py b/datasette/views/table.py
index 035abb1b..cf5b5b64 100644
--- a/datasette/views/table.py
+++ b/datasette/views/table.py
@@ -369,6 +369,7 @@ async def display_columns_and_rows(
                 "is_pk": False,
                 "type": "",
                 "notnull": 0,
+                "is_special_link_column": True,
             }
         columns = [first_column] + columns
     return columns, cell_rows
diff --git a/tests/test_table_html.py b/tests/test_table_html.py
index a39df25d..d8dde593 100644
--- a/tests/test_table_html.py
+++ b/tests/test_table_html.py
@@ -248,6 +248,7 @@ async def test_sort_links(ds_client):
                 "data-column-type": "",
                 "data-column-not-null": "0",
                 "data-is-pk": "0",
+                "data-is-link-column": "1",
             },
             "a_href": None,
         },