Multiple-cluster schemes, such as cluster adaptive training (CAT) or eigenvoice systems, are a popular approach for rapid speaker and environment adaptation. Interpolation weights are used to transform a multiple-cluster, canonical, model to a standard hidden Markov model (HMM) set representative of an individual speaker or acoustic environment. Maximum likelihood training for CAT has previously been investigated. However, in state-of-the-art large vocabulary continuous speech recognition systems, discriminative training is commonly employed. This paper investigates applying discriminative training to multiple-cluster systems. In particular, minimum phone error (MPE) update formulae for CAT systems are derived. In order to use MPE in this case, modifications to the standard MPE smoothing function and the prior distribution associated with MPE training are required. A more complex adaptive training scheme combining both interpolation weights and linear transforms, a structured transform (ST), is also discussed within the MPE training framework. Discriminatively trained CAT and ST systems were evaluated on a state-of-the-art conversational telephone speech task. These multiple-cluster systems were found to outperform both standard and adaptively trained systems