Bit rate adaptation is one of the most important types of video transcoding. With H. 264 becoming the predominant video codec of choice in video coding and streaming, prudent rate-adaptation techniques should be developed. In this paper, we investigate certain critical points in the spectrum of rate shaping requests. We show that the selection of quantization step sizes may not have monotonic effects on rate-distortion characteristics in the transcoding sense. In other words, distortion in the regular sense can be different from the distortion in the context of transcoding in which a requantization process is carried out. We show in a generic form that careful selections of the step size can lead to much improved performance. Experiments based on both simulation and real transcoding show the effectiveness of the proposed solution.