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In recent years a better understanding of the magnetic recording process has resulted from self-consistent iterative calculations of the magnetization transition induced in the recording medium. One important limitation on these calculations has been the difficulty in fitting realistic hysteresis loops into these calculations. It is not practical to include the actual hysteresis loops, so the practice has been to approximate them by various plausible models. However, none of these models fit the actual loops as closely as would be desired. In this paper, we avoid modelling the major loops, but approximate them using spline interpolation. We demonstrate, by comparison with experimental loops, that the actual loops can be approximated much more closely than with an analytic model. A criterion for deriving the minor loops is given, and we demonstrate a generally better fit of the initial minor loops than that obtained from a model. A self-consistent iterative calculation is made using both an analytic model and the spline approximated loops. We find that the choice of loop model noticeably affects the calculated magnetization distribution and that the spline approximated loops lead to a transition width which more closely matches the width estimated from an experimental single readback pulse. In summary, we demonstrate that good simulation of the hysteresis loops can be significant and discuss a simple approximation technique from which an excellent fit to actual loops can be obtained.