In situations when automatic speech recognition (ASR) systems are rapidly deployed for a new task, the availability of within-domain training data may be limited. In such cases one needs to build the ASR system from other, possibly out-of-domain databases. We refer to the process of building ASR systems for one task domain using data from other domains as cross-domain modelling or CDM. Conventional CDM-based systems perform poorly because the disparity between the triphonetic distributions of the training and test domains is not well accounted for. In this paper we describe two techniques to impose the acousticphonetic structure of the task domain on acoustic models built from out-of-domain data. The first technique, called Extrinsic CDM, combines decision tree structures obtained from a database close in domain to the task domain with acoustic models that are trained from a third less domain-relevant database. In the second technique, called Intrinsic CDM, the task domain data is used to impose the triphonetic distribution of the task domain on the decision trees built from an out-of-domain large database. Both these techniques result in acoustic models which perform better than conventional CDM models.