[Haskell-cafe] Feeding a monad into itself

I have a function f :: a -> Maybe a that I want to feed into itself with some initial input until it returns Nothing. untilNothing :: (a -> Maybe a) -> a -> a untilNothing f x = case f x of Just x' -> untilNothing f x' Nothing -> x Is there a better way to do this? I feel like there is something more general going on with Monads being fed into themselves, but maybe I'm wrong. Thoughts?