In a bid to enhance the search performance, this paper presents an improved version of reduced candidate mechanism (RCM), an algebraic codebook search conducted on an algebraic code‐excited linear‐prediction (ACELP) speech coder. This improvement is made on the basis of two findings in our prior work. The first finding is that a pulse with a high contribution in the associated track is more likely to serve as the optimal pulse in the optimal codevector; the second is that the speech quality can be well maintained at a search accuracy above 50% approximately. Subsequently, a new finding in this study is that there is a 0.8321 probability that the No. 1 ranked pulse in a global sorting by pulse contribution is indeed one of the optimal pulses. Hence, the No. 1 pulse in the global sorting is labeled as one of the optimal pulses, following which a sequence of search tasks is fulfilled through RCM. This proposed complexity reduction algorithm, implemented on a G.729A speech codec, takes as few as eight searches, a search load amounting to 2.5% of G.729A, 12.5% of global pulse replacement method (iteration = 2), 16.7% of iteration‐free pulse replacement method, and 50% of RCM (N = 2). This proposal is thus found to successfully reduce the required computational complexity to a great extent as intended. © 2014 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.