The problem of analyzing an initialized loop and verifying that the program computes some particular function of its inputs is addressed. A heuristic technique for solving these problems is proposed that appears to work well in many commonly occurring cases. The use of the technique is illustrated with a number of applications. An attribute of initialized loops is identified that corresponds to the ``effort'' required to apply this method in a deterministic (i.e., guaranteed to succeed) manner. It is explained that in any case, the success of the proposed heuristic relies on the loop exhibiting a ``reasonable'' form of behavior.