Abstract Minimalism emphasizes the simplicity of UG and the role of computational efficiency as a third factor that shapes grammar. But how does one turn this big-picture idea into a concrete proposal with specific predictions? This talk presents a computational answer in the form a simple processing model for Minimalism that 1) unifies a broad range of phenomena from relative clause processing to heavy NP shift and quantifier scope preferences, and 2) suggests hard limits on the complexity of syntax, thereby deriving a number of island constraints.