An analytical study is made of simple models of steady fronts in the atmosphere in which the temperature field is subjected to deformation as the fluid moves downstream in a large-scale horizontal flow. One fundamental approximation is made and then a Lagrangian method, in which fluid particles are identified by conservation of entropy and potential vorticity, and by Bernoulli's theorem, enables the steady problem to be solved. Solutions for models of surface fronts and upper tropospheric fronts are compared with those obtained from a model in which there is no variation along the front and the frontogenesis proceeds in time. If the thermal wind is comparable with the basic wind, and the potential vorticity is not negligible in some sense, the frontogenesis is increased where the thermal wind opposes the basic flow but, decreased where it reinforces the flow.