This paper addresses the problem of building an interruptible real-time system using contract algorithms. Contract algorithms offer a tradeoff between computation time and quality of results, but their run-time must be determined when they are activated. Many AI techniques provide useful contract algorithms that are not interruptible. We show how to optimally sequence contract algorithms to create the best interruptible system with or without stochastic information about the deadline. These results extend the foundation of real-time problem-solving and provide useful guidance for embedding contract algorithms in applications.