The paper details all aspects of the CUHTK 2004 Mandarin conversational telephone speech transcription system, but concentrates on the development of the acoustic models. As there are significant differences between the available training corpora, both in terms of topics of conversation and accents, forms of data normalisation and adaptive training techniques are investigated. The baseline discriminatively trained acoustic models are compared to a system built with a Gaussianisation front-end, a speaker adaptively trained system and an adaptively trained structured precision matrix system. The models are finally evaluated within a multi-pass, multi-branch, system combination framework.