diff --git a/datasette/templates/_table.html b/datasette/templates/_table.html
index ba34b60f..f47a325f 100644
--- a/datasette/templates/_table.html
+++ b/datasette/templates/_table.html
@@ -1,6 +1,6 @@
 <!-- above-table-panel is a hook node for plugins to attach to . Displays even if no data available -->
 <div class="above-table-panel"> </div>
-{% if display_rows %}
+{% if display_columns %}
 <div class="table-wrapper">
     <table class="rows-and-columns">
         <thead>
@@ -31,6 +31,7 @@
         </tbody>
     </table>
 </div>
-{% else %}
+{% endif %}
+{% if not display_rows %}
     <p class="zero-results">0 records</p>
 {% endif %}
diff --git a/datasette/templates/table.html b/datasette/templates/table.html
index 2919d306..c841e1be 100644
--- a/datasette/templates/table.html
+++ b/datasette/templates/table.html
@@ -141,7 +141,6 @@
 {% if all_columns %}
 <column-chooser></column-chooser>
 <button class="choose-columns-mobile small-screen-only" onclick="openColumnChooser()">Choose columns</button>
-{% if display_rows %}
 <button type="button" class="column-actions-mobile small-screen-only">
     <svg aria-hidden="true" xmlns="http://www.w3.org/2000/svg" width="14" height="14" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round">
         <circle cx="12" cy="12" r="3"></circle>
@@ -149,7 +148,6 @@
     </svg>
     <span>Column actions</span>
 </button>
-{% endif %}
 <script>
 window._columnChooserData = {{ {"allColumns": all_columns, "selectedColumns": display_columns|map(attribute='name')|list, "primaryKeys": primary_keys}|tojson }};
 </script>
diff --git a/tests/test_html.py b/tests/test_html.py
index e38898da..7425692d 100644
--- a/tests/test_html.py
+++ b/tests/test_html.py
@@ -805,7 +805,7 @@ async def test_blob_download_invalid_messages(ds_client, path, expected_message)
 async def test_zero_results(ds_client, path):
     response = await ds_client.get(path)
     soup = Soup(response.text, "html.parser")
-    assert 0 == len(soup.select("table"))
+    assert 0 == len(soup.select("table tbody tr"))
     assert 1 == len(soup.select("p.zero-results"))
 
 
diff --git a/tests/test_table_html.py b/tests/test_table_html.py
index d8dde593..86b9a4eb 100644
--- a/tests/test_table_html.py
+++ b/tests/test_table_html.py
@@ -752,8 +752,11 @@ async def test_column_chooser_present(ds_client):
 
 
 @pytest.mark.asyncio
-async def test_mobile_column_actions_present(ds_client):
-    response = await ds_client.get("/fixtures/facetable")
+@pytest.mark.parametrize(
+    "path", ["/fixtures/facetable", "/fixtures/123_starts_with_digits"]
+)
+async def test_mobile_column_actions_present(ds_client, path):
+    response = await ds_client.get(path)
     assert response.status_code == 200
     soup = Soup(response.text, "html.parser")
     button = soup.select_one("button.column-actions-mobile.small-screen-only")
@@ -764,6 +767,25 @@ async def test_mobile_column_actions_present(ds_client):
         "mobile-column-actions.js" in (script.get("src") or "")
         for script in soup.find_all("script")
     )
+    # mobile-column-actions.js builds its dialog from <th data-column> elements,
+    # so the thead must render even when the table has no rows.
+    ths = soup.select("table.rows-and-columns thead th[data-column]")
+    assert len(ths) >= 1
+
+
+@pytest.mark.asyncio
+async def test_zero_row_table_renders_thead(ds_client):
+    response = await ds_client.get("/fixtures/123_starts_with_digits")
+    assert response.status_code == 200
+    soup = Soup(response.text, "html.parser")
+    table = soup.select_one("table.rows-and-columns")
+    assert table is not None
+    column_names = [
+        th.get("data-column") for th in table.select("thead th[data-column]")
+    ]
+    assert "content" in column_names
+    assert table.select_one("tbody tr") is None
+    assert soup.select_one("p.zero-results") is not None
 
 
 @pytest.mark.asyncio