In this paper we introduceStrategy Logic with Sim-ple Goals(SL[SG]), a fragment of Strategy Logicthat strictly extends the well-known Alternating-time Temporal LogicATLby introducing arbitraryquantification over the agents’ strategies. Our mo-tivation comes from game-theoretic applications,such as expressing Stackelberg equilibria in games,coercion in voting protocols, as well as modulechecking for simple goals. Most importantly, weprove that the model checking problem forSL[SG]isP-complete, the same asATL. Thus, the extraexpressive power comes at no computational costas far as verification is concerned.