How do children learn a verb's argument structure when their input contains clause types that obscure verb transitivity? A child might infer that throw is transitive by observing that it occurs in sentences with direct objects (e.g. Amy threw a frisbee), but this strategy is complicated by "non-basic" clauses where the argument acting as the verb's object doesn't occur after the verb (e.g. Which frisbee did Amy throw __?). In this talk I'll focus on a frequent type of non-basic clause: filler-gap dependencies, which include wh-questions and relative clauses. I'll present preliminary data from an ongoing study on children's acquisition of these dependencies in English, and discuss how identifying these dependencies interacts with verb argument structure acquisition. I'll then present a computational model that can learn verb transitivity by inferring how to filter these non-basic clauses from its input, without having to identify them first.