Fault-tolerant computer networks rely on mechanisms supporting the fast detection of link failures. Tomo-graphic techniques can be used to implement such mechanisms at low cost: it is often sufficient to deploy a small number of tomography nodes exchanging probe messages along paths between them and detect link failures based on these messages. Our paper studies a practically relevant aspect of network tomography: the impact of the routing model. While the relevance of the routing model on path diversity and hence tomog-raphy cost is obvious and well-known on an anecdotal level, we lack an analytical framework to quantify the influence of different routing models (such as destination-based routing) exists. This paper fills this gap and introduces a formal model for asymmetric network tomography and a taxonomy of path routing models. This facilitates algorithmic reasoning about tomographic placement problems and quantifying the difference between routing models. In particular, we provide optimal and near-optimal algorithms to deploy a minimal number of asymmetric and symmetric tomography nodes for basic network topologies (modelled as graphs) under different routing model classes. Interestingly, we find that in many cases routing according to a more restrictive routing model gives better results: compared to a more general routing model, computing a good placement is algorithmically more tractable and does not entail high monitoring costs, a desirable trade-off in practice.