Abstract We consider the setting in which executions of contract algorithms are scheduled in a processor so as to produce an interruptible system. Such algorithms offer a trade off between the quality of output and the available computation time, provided that the latter is known in advance. Previous work on this setting has provided strict performance guarantees for several variants of this setting, assuming that an interruption can occur arbitrarily ahead in the future. In practice, however, one expects that the schedule will reach a point beyond which further progress will only be marginal, hence it can be deemed complete. In this work we show how to optimize the time at which the system reaches a desired performance objective, while maintaining interruptible guarantees throughout the entire execution. The resulting schedule is provably optimal, and it guarantees that upon completion each individual contract algorithm has attained a predefined end guarantee