Out-of-order execution and branch prediction are two mechanisms that can be used profitably in the design of Supercomputers to increase performance. Unfortunately this means there must be some kind of repair mechanism, since situations do occur that require the computing engine to repair to a known previous state. One way to handle this is by checkpoint repair. In this paper we derive several properties of checkpoint repair mechanisms. In addition, we provide algorithms for performing checkpoint repair that incur very little overhead in time and modest cost in hardware. We also note that our algorithms require no additional complexity or time for use with write back cache memory systems than they do with write through cache memory systems, contrary to statements made by previous researchers.