Numerical model calculations relating to the motion of a baroclinic vortex in a vertical shear flow exhibit a rich behaviour. We have shown previously that much of this behaviour can be understood in terms of a simple two-layer model in which the vortex is idealized by a line vortex or a distributed vortex in each layer. In this model, the component vortices in each layer suffer advection by the flow in that layer and by a fraction of the tangential flow of the other vortex at their centre, but they are not allowed to distort. The idealization leads to a set of four coupled ordinary differential equations which are easily solved. We show here that the solutions compare well with numerical integrations of the full partial differential equations in the case of quasi-geostrophic vortices for a certain period of time. Further, they help to understand qualitatively the regimes of behaviour that occur in the quasi-geostrophic calculations, and also in calculations for more intense vortices, where there is a mutual deformation of the component vortices