This paper describes a method for hands-free speech recognition, and particularly for the simultaneous recognition of multiple sound sources. The method is based on the 3-D Viterbi search, i.e., extended to the 3-D N-best search method enabling the recognition of multiple sound sources. The baseline system integrates two existing technologies--3-D Viterbi search and conventional N-best search--into a complete system. Previously, the first evaluation of the 3-D N-best search-based system showed that new ideas are necessary to develop a system for the simultaneous recognition of multiple sound sources. It found two factors that play important roles in the performance of the system, namely the different likelihood ranges of the sound sources and the direction-based separation of the hypotheses. In order to solve these problems, we implemented a likelihood normalization and a path distance-based clustering technique into the baseline 3-D N-best search-based system. The performance of our system was evaluated through experiments on simulated data for the case of two talkers. The experiments showed significant improvements by implementing the above two techniques. The best results were obtained by implementing the two techniques and using a microphone array composed of 32 channels. More specifically, the Word Accuracy for the two talkers was higher than 80% and the Simultaneous Word Accuracy (where both sources are correctly recognized simultaneously) was higher than 70%, which are very promising results.