In the normal course of events, children manifest linguistic competence equivalent to that of local adults in just a few years. Children can produce and understand novel sentences, they can judge that certain strings of words are true or false, and so on. Yet experience appears to dramatically underdetermine the competence children so rapidly achieve, even given optimistic assumptions about children’s nonlinguistic capacities to extract information and form generalizations on the basis of statistical regularities in the data they receive. These considerations underlie various (more specific) poverty-of-stimulus arguments for the innate specification of linguistic principles. But in our view, certain features of nativist arguments have not yet been fully appreciated. We focus here on three (related) kinds of poverty-of-stimulus argument, each of which has been supported by the findings of psycholinguistic investigations of child language.