Heuristic search procedures are useful in a large number of problems of practical importance. Such procedures operate by searching several paths in a search space at the same time, expanding some paths more quickly than others depending on which paths look most promising. Often large amounts of time are required in keeping track of the information control knowledge. For some problems, this overhead can be greatly reduced by preprocessing the problem in appropriate ways. In particular, we discuss a data structure called a threaded decision graph, which can be created by preprocessing the search space for some problems, and which captures the control knowledge for problem solving. We show how this can be done, and we present an analysis showing that by using such a method, a great deal of time can be saved during problem solving processes.