Each time I find myself needing to use the wrapping functions necessary for this embeddings, I grumble. Does anyone have a favorite use-pattern for ameliorating these quickly ubiquitous conversions? For runKleisli, I was considering something like okKleisli :: (Control.Arrow.Kleisli m a b -> Control.Arrow.Kleisli m' a' b') -> (a -> m b) -> (a' -> m' b') onKleisli f = Control.Arrow.runKleisli . f . Control.Arrow.Kleisli but haven't really tested its usefulness. My most frequent use cases usually include Arrow.first, Arrow.second, &&&, ***, or +++. E.g. somefun :: (Monad m, Num a) => (a, d) -> m (a, d) somefun = onKleisli Control.Arrow.first (\ a -> return (a + 1)) Perhaps a Control.Arrow.Kleisli, which would export (same-named) Kleisli specializations of all the Control.Arrow methods? And an analogous Control.Applicative.Monad? (Data.Traversable does this a little bit to specialize its interface for monads, such as Data.Traversable.sequence.) While writing this, I realized that you can't leave the Arrow-ness of Kleisli arrows implicit, since (->) a (m b) is two kinds of arrows depending on context -- which is precisely what the Kleisli newtype resolves. So I'm not seeing a reason to bring up the 'class Applicative m => Monad m where' dispute. Thanks for your time.