The typical approach to steganography is to compress the covert data in order to limit its size, which is reasonable in the context of a limited steganographic bandwidth. TranSteg (Trancoding Steganography) is a new IP telephony steganographic method that was recently proposed that offers high steganographic bandwidth while retaining good voice quality. In TranSteg, compression of the overt data is used to make space for the steganogram. In this paper we focus on analyzing the influence of the selection of speech codecs on hidden transmission performance, that is, which codecs would be the most advantageous ones for TranSteg. Therefore, by considering the codecs which are currently most popular for IP telephony we aim to find out which codecs should be chosen for transcoding to minimize the negative influence on voice quality while maximizing the obtained steganographic bandwidth.