This paper investigates some problems encountered in the all-pass watermarking scheme developed by Yardymcy et al. [II and suggest ways to eliminate it. The system under consideration uses all-pass filters to embed data into a speech or music signal by phase modification in consecutive blocks. Some artefacts in doing so. The two approaches we suggest in this paper remove these artefacts while keeping the watermark detectable and all the advantages of the method. The results of the experimental studies related to the relation between the block length, and perceptibility and misdetection rate are presented. Studies are carried out to determine the immunity against additive noise and ways are suggested to improve it.