Cross-matching catalogues from radio surveys to catalogues of sources at other wavelengths is extremely hard, because radio sources are often extended, often consist of several spatially separated components, and often no radio component is coincident with the optical/infrared host galaxy. Traditionally, the cross-matching is done by eye, but this does not scale to the millions of radio sources expected from the next generation of radio surveys. We present an innovative automated procedure, using Bayesian hypothesis testing, that models trial radio-source morphologies with putative positions of the host galaxy. This new algorithm differs from an earlier version by allowing more complex radio-source morphologies, and performing a simultaneous fit over a large field. We show that this technique performs well in an unsupervised mode.