The physical basis and a mathematical formulation of a softening model nicknamed Alsoft, accounting for the combined effect of recovery and recrystallization during annealing of heavily deformed aluminium alloys have been presented. The prediction power of the model is tested against experiments in terms of softening kinetics and final grain structure of selected Al-Mn-Fe-Si-model alloys with different as homogenized microchemistries in terms solid solution levels of Mn (potential of concurrent precipitation) and different constituent particle and dispersoid structures. It is demonstrated that good model predictions may be obtained for alloys and conditions which are not or too a limited extent influenced by particle drag effects and concurrent precipitation while conditions strongly affected by these effects are increasingly difficult to model and in the most extreme cases impossible with reasonable input model parameters.