The article examines the performance of the efficiency-adjusted deferred acceptance mechanism (EADAM) compared to the deferred acceptance mechanism (DA) in school choice. It finds that EADAM leads to higher efficiency and truth-telling rates than DA, even though EADAM is not strategy-proof. When priority waivers are enforced, efficiency increases further, while truth-telling rates decrease. These results challenge the importance of strategy-proofness in ensuring truth-telling and suggest a new trade-off between efficiency and vulnerability to preference manipulation. The study also explores how default rules affect consent rates and efficiency under EADAM. It finds that more than half of the students consent to waive their priorities, consistent with evidence on costless altruism. The research contributes to market design and behavioral economics, showing that non-strategy-proof mechanisms can yield higher truth-telling rates. The findings suggest that strategy-proofness may be less important for optimal matching in school choice than previously thought. The study also highlights the challenges of implementing complex algorithms in real-world settings and the potential for post-allocation trading to improve efficiency, though it risks preference manipulation. The results have implications for policy makers aiming to balance efficiency and fairness in school admissions.The article examines the performance of the efficiency-adjusted deferred acceptance mechanism (EADAM) compared to the deferred acceptance mechanism (DA) in school choice. It finds that EADAM leads to higher efficiency and truth-telling rates than DA, even though EADAM is not strategy-proof. When priority waivers are enforced, efficiency increases further, while truth-telling rates decrease. These results challenge the importance of strategy-proofness in ensuring truth-telling and suggest a new trade-off between efficiency and vulnerability to preference manipulation. The study also explores how default rules affect consent rates and efficiency under EADAM. It finds that more than half of the students consent to waive their priorities, consistent with evidence on costless altruism. The research contributes to market design and behavioral economics, showing that non-strategy-proof mechanisms can yield higher truth-telling rates. The findings suggest that strategy-proofness may be less important for optimal matching in school choice than previously thought. The study also highlights the challenges of implementing complex algorithms in real-world settings and the potential for post-allocation trading to improve efficiency, though it risks preference manipulation. The results have implications for policy makers aiming to balance efficiency and fairness in school admissions.