Superconductors of type-II are partially penetrated by magnetic flux, where the pinning of flux tubes constitutes a memory that gives rise to a hysteresis. However, the hysteresis gradually disappears when a transport current approaches the critical current. This paper investigates what possibilities and limitations the Preisach model has to describe this hysteresis. Previous results are complimented by demonstrating the limitation to higher harmonics, the computation of an inverse model including an inductive part, and by modelling the gradual disappearing hysteresis with a saturation.