Threading monads

Occasionally I have a non-monadic function (call it "x") that takes a function (call it "y") as an argument and uses it for stuff. Then, one day I inevitably want to pass it a y that needs to do something monadically: e.g. when I wanted unfoldM instead of unfoldr. So, I have to rewrite x accordingly. If I want to write an x that is open to taking a monadic y but doesn't require it to be monadic, should I maybe write it monadically and provide a wrapper that puts non-monadic y's in the Identity monad? Might this wrapping approach cause less efficient code than writing an alternative non-monadic x for non-monadic y's? Am I making any sense at all? (-: -- Mark