I've got a covered litterbox with a door. Bought the biggest there was, because Sirius was such a clumsy perfectionist on the regular sized one. His size combined with his clumsiness just did make that one way too small for him. He'd be scratching for ages before dropping the items and then scratch for ages again, attempting to cover the shit.
Bigger box made him behave like an ordinary cat. And we did not have loads of grit scooped everywhere because of his excessive scratching anymore.