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 based on two findings in a piece of our prior work. The first finding is that a pulse with a high contribution in the associated track is more likely to serve as an optimal pulse in the optimal codevector and 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 concerning a structured algebraic codebook in G.729 indicates that there is a 0.8321 probability that the number 1 ranked pulse in a global sorting by pulse contribution is indeed one of the optimal pulses. Hence, the number 1 pulse in the global sorting is labeled as one of the optimal pulses, following which a sequence of search tasks are fulfilled through RCM. This proposed complexity reduction algorithm, implemented on a G.729A speech codec, takes as few as eight searches, a search load tantamount 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.