The paper presents a new steganographic method for IP telephony called TranSteg (Transcoding Steganography). Typically, in steganographic communication it is advised for covert data to be compressed in order to limit its size. In TranSteg it is the overt data that is compressed to make space for the steganogram. The main innovation of TranSteg is to, for a chosen voice stream, find a codec that will result in a similar voice quality but smaller voice payload size than the originally selected. Then, the voice stream is transcoded. At this step the original voice payload size is intentionally unaltered and the change of the codec is not indicated. Instead, after placing the transcoded voice payload, the remaining free space is filled with hidden data. TranSteg proof of concept implementation was designed and developed. The obtained experimental results are enclosed in this paper. They prove that the proposed method is feasible and offers a high steganographic bandwidth while introducing small voice degradation. Moreover, TranSteg detection is difficult to perform when compared with existing VoIP steganography methods.