A new video coding standard H.264/AVC has been recently developed and standardized. The standard represents a number of advances in video coding technology in terms of both coding efficiency and flexibility and is expected to replace the existing standards such as H.263 and MPEG-1/2/4 in many possible applications. In this paper we investigate and present efficient syntax transcoding and downsizing transcoding methods from H.263 to H.264/AVC standard. Specifically, we propose an efficient motion vector reestimation scheme using vector median filtering and a fast intraprediction mode selection scheme based on coarse edge information obtained from integer-transform coefficients. Furthermore, an enhanced rate control method based on a quadratic model is proposed for selecting quantization parameters at the sequence and frame levels together with a new frame-layer bit allocation scheme based on the side information in the precoded video. Extensive experiments have been conducted and the results show the efficiency and effectiveness of the proposed methods.