Thanks for the replies. I think that last one is the way I'll have to go.
I just ask, because in the future, with more complex objects/characters, it would be good to know. So if I've got, say, a character whose chest I want to be visibly breathing, and then I want to walk him around, I'd like that localized breathing-animation to loop infinitely while I move the character around globally.
I know there's a way to do this, I just can't find it.