diff --git a/datasette/renderer.py b/datasette/renderer.py
index 0e01f52f..bb53f13a 100644
--- a/datasette/renderer.py
+++ b/datasette/renderer.py
@@ -6,7 +6,6 @@ from datasette.utils import (
     error_body,
     path_from_row_pks,
     remove_infinites,
-    sqlite3,
     value_as_boolean,
 )
 from datasette.utils.asgi import Response
@@ -59,13 +58,11 @@ def json_renderer(request, args, data, error, truncated=None):
     if truncated is not None:
         data["truncated"] = truncated
     if shape == "arrayfirst":
-        if not data["rows"]:
-            data = []
-        elif isinstance(data["rows"][0], sqlite3.Row):
-            data = [row[0] for row in data["rows"]]
-        else:
-            assert isinstance(data["rows"][0], dict)
-            data = [next(iter(row.values())) for row in data["rows"]]
+        # Rows can be dicts, sqlite3.Row or lists (from remove_infinites)
+        data = [
+            next(iter(row.values())) if isinstance(row, dict) else row[0]
+            for row in data["rows"]
+        ]
     elif shape in ("objects", "object", "array"):
         columns = data.get("columns")
         rows = data.get("rows")
@@ -94,12 +91,10 @@ def json_renderer(request, args, data, error, truncated=None):
             data = data["rows"]
 
     elif shape == "arrays":
-        if not data["rows"]:
-            pass
-        elif isinstance(data["rows"][0], sqlite3.Row):
-            data["rows"] = [list(row) for row in data["rows"]]
-        else:
-            data["rows"] = [list(row.values()) for row in data["rows"]]
+        data["rows"] = [
+            list(row.values()) if isinstance(row, dict) else list(row)
+            for row in data["rows"]
+        ]
     else:
         status_code = 400
         data = error_body(f"Invalid _shape: {shape}", status_code)
diff --git a/tests/test_table_api.py b/tests/test_table_api.py
index 58a5ddc3..73cad460 100644
--- a/tests/test_table_api.py
+++ b/tests/test_table_api.py
@@ -1302,6 +1302,24 @@ async def test_infinity_returned_as_invalid_json_if_requested(ds_client):
     ]
 
 
+@pytest.mark.asyncio
+@pytest.mark.parametrize(
+    "shape,expected",
+    (
+        ("arrays", {"ok": True, "rows": [[None], [None], [1.5]], "truncated": False}),
+        ("arrayfirst", [None, None, 1.5]),
+    ),
+)
+async def test_infinity_with_array_shapes(ds_client, shape, expected):
+    # Rows containing infinity are lists rather than sqlite3.Row objects
+    response = await ds_client.get(
+        "/fixtures/-/query.json?sql=select+value+from+infinity+order+by+rowid"
+        "&_shape=" + shape
+    )
+    assert response.status_code == 200
+    assert response.json() == expected
+
+
 @pytest.mark.asyncio
 async def test_custom_query_with_unicode_characters(ds_client):
     # /fixtures/𝐜𝐢𝐭𝐢𝐞𝐬.json