I have proposed a method for detecting local slower phrases in Japanese spontaneous conversational speech. A threshold is applied to phrase-averaged mora duration in this method. It is considered that relative variation of time sequence of phrase-averaged mora duration should be taken into account for detecting slower phrases correctly. In this paper, preliminary experiments are carried out to obtain optimal threshold. Then the optimal threshold is applied to Japanese conversational speech. I have confirmed that the threshold in consideration of relative variation of phrase-averaged mora duration has better result than the simple straight threshold.