An increasingly popular practice for student assignment to public schools in the U.S. is the use of school choice systems. The celebrated Gale-Shapley student-optimal stable mechanism (SOSM) has recently replaced two de…ficient student assignment mechanisms that were in use in New York City and Boston. We provide theoretical evidence that the SOSM outcome may produce large welfare losses. Then we propose an efficiency adjusted deferred acceptance mechanism (EADAM) that allows a student to consent to waive a certain priority that has no effect on his assignment. Under EADAM a consenting student causes himself no harm, but may help many others bene…fit as a consequence. We show that EADAM can recover any welfare losses due to SOSM while also preserving immunity against strategic behavior in a particular way. It is also possible to use EADAM to eliminate welfare losses due to randomly breaking ties in student priorities. I