We present models of the submillimetre dust emission around four Vega-excess stars. The results are adjusted to fit simultaneously the spectral energy distribution from millimetre through to optical wavelengths, as well as the submillimetre image. The combination of spatially resolved images with continuum fluxes over a range of wavelengths can remove some of the previous ambiguities in estimating the dust emission characteristics and circumstellar distributions. Fomalhaut shows the brightest and best-resolved submillimetre image, and so gives the most unambiguous fit. Both the imaging and photometric results can best be modelled by an edge-on thick torus, of inner radius 100 au, outer radius 140 au and thickness ∼120 au. The observed sharp outer boundary cannot be fitted by a reasonable power-law density distribution. Furthermore, inside 100 au the density also drops abruptly, by at least a factor of 10. The structures of Vega and ε Eri are also best modelled by radially thin rings rather than discs, in both cases viewed almost pole-on. However, there are clearly clumps in their morphologies which cannot be explained by simple axisymmetric models. The submillimetre disc in β Pic can be adequately fitted by the same model as that used to account for the extended structure seen in scattered light. However, the additional south-western emission component, if it lies in the β Pic system, must have a dust mass comparable to that of the whole visible disc. In all cases, the spectral energy distribution can be fitted by a single ring or disc-like structure. Grain sizes of a few tens of μm and β=0.8–1.1 provide the best fits, and we place limits on the dust size distribution. The dust temperatures are too low and there is too much temperature variation between the sources for grain sublimation to be effective at creating the central holes. All rings are dominated by grain-grain collisions, and we discuss methods of creating and sustaining the observed structures. Most likely they arise from a mechanism such as planet shepherding. The outer cut-off may arise in a similar way, although external stripping of material is not discounted.