Dynamic programming is a powerful technique for solving optimization problems efficiently. We consider a dynamic program as simply a recursive program that is evaluated with memoization and lookup of answers. In this paper we examine how, given a function calculating a bound on the value of the dynamic program, we can optimize the compilation of the dynamic program function. We show how to automatically transform a dynamic program to a number of more efficient versions making use of the bounds function. We compare the different transformed versions on a number of example dynamic programs, and show the benefits in search space and time that can result.