Adjustments are described that should be made to a single filament description of a tokamak plasma if accurate modelling of a non-linear MHD simulation is to be achieved. It is shown that although the single filament model is excellent for purely radial, or purely vertical, fields, it does not describe the gradients of these fields. A simple scalar correction to the gradient terms in the model is found to facilitate the accurate prediction of the growth rate of the vertical instability. An extension to the modelling of X points is also presented. The corrected multi-pole model is shown to be appropriate for the design of robust controllers