Truthful revelation of preferences has emerged as a desideratum in the design of school choice programs. Gale-Shapley's deferred acceptance mechanism is strategy-proof for students but limits their ability to communicate their preference intensities. This results in ex-ante inefficiency when ties at school preferences are broken randomly. We propose a variant of deferred acceptance mechanism which allows students to influence how they are treated in ties. It maintains truthful revelation of ordinal preferences and supports a greater scope of efficiency.