In this paper we study the tone reservation technique for the reduction of the peak to average power ratio (PAPR) in code division multiple access (CDMA) systems that employ the Walsh functions. In the tone reservation method, the available carriers are partitioned into two sets, the information set, which carries the information, and the compensation set, which is used to reduce the PAPR. Central questions are: What is the best possible reduction of the PAPR? What is the optimal information set that achieves this reduction, and how can it be found? What is the general structure of the information set? So far, the answers were unknown. In this paper we completely solve these questions for CDMA systems that employ the Walsh functions. Interestingly, using the first N Rademacher functions is optimal under all sets of size N.