In multimedia communication, due to the limited computational capability of the personal information machine, a coder with low computational complexity is needed to integrate services from several media sources. This paper presents two efficient candidate schemes to simplify the most computationally demanding operation, the excitation codebook search procedure. For fast adaptive codebook search, we propose an algorithm that uses residual signals to predict the candidate gain-vectors of the adaptive codebook. For the fixed codebook, we propose a fast search algorithm using an energy function to predict the candidate pulses, and we redesign the codebook structure to twin multi-track positions architecture. Overall simulation results indicate that the average perceptual evaluation of speech quality (PESQ) score is degraded slightly, by 0.049, and our proposed methods can reduce total computational complexity by about 67% relative to the original G.723.1 encoder computation load, and with perceptually negligible degradation. Objective and subjective evaluations verify that the more efficient candidate schemes we propose can provide speech quality comparable to that using the original coder approach.