Gale-Shapley's deferred acceptance (henceforth DA) mechanism has emerged as a prominent candidate for placing students to public schools. While DA has desirable fairness and incentive properties, it limits the applicants' abilities to communicate their preference intensities, which entails ex ante inefficiency when ties at school preferences are broken randomly. We propose a variant of deferred acceptance mechanism that allows students to influence how they are treated in ties. It inherits much of the desirable properties of DA but performs better in ex ante efficiency. (JEL D82, H75, I21, I28)