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This paper addresses the following question: what is the minimum-sized synchronous window needed to solve consensus in an otherwise asynchronous system? In answer to this question, we present the first optimally-resilient algorithm ASAPthat solves consensus as soon as possiblein an eventually synchronous system, i.e., a system that from some time GSTonwards, delivers messages in a timely fashion. ASAPguarantees that, in an execution with at most ffailures, every process decides no later than round GST+ f+ 2, which is optimal.