The introduction of the concept of sequential decoding by Wozencraft has opened up the possibility of more efficient decoding search procedures than those available with block codes. The purpose of this study is to improve the search procedures proposed by Pfeiffer and Lin. We show that under most error conditions it is not required to begin the search at the earliest segment in the br-unit indicated by the multiple threshold test. An improved estimate of the probability of correcting an error in a br-unit is given. A new backup procedure and a modified threshold for discard make possible a more efficient search for the best path.