HSEARCH and LSEARCH were originally formulated in the framework of universal Turing machines with potentially infinite storage. Hence these methods may largely ignore questions of storage management. Realistic computers, however, have limited storage. So we need to efficiently reset storage modifications computed by the numerous programs OOPS is testing. Furthermore, our programs typically will be composed from primitive instructions that are more complex and time-consuming than those of typical Turing machines. In what follows we will address such issues in detail.