Universal Grammar, it is often said, consists of principles and a set of option-points or parameters. If this is so, then we need a separate theory that will complement UG in order to yield an account of language acquisition; specifically, something needs to be said about how parameters are set. I argue here for a principle of degree-0 learnability, which says something about how parameters are set and does not belong to Universal Grammar, if UG consists only of grammatical principles and parameters. The idea is that parameters are set only by structurally simple data. I contrast this idea with another proposal in the literature, which addresses some similar problems: the idea that children set their parameters primarily on the basis of data from embedded clauses (Roeper & Weissenborn, 1990).