AbstractSelf-affine and piecewise self-affine IFS fractal models are used in this paper to model several different types of discrete sequences. The parameters of such models are determined according to an optimizar tion criterion. However, the general optimization problem is quite complex, and therefore some constraints are introduced. The best tradeoff between overall performance and computational complexity is found. The optimal estimation of the fractal models parameters is obtained by means of genetic algorithms, and a very good convergence to the global minimum is obtained with a proper tuning of the algorithm. A comparison with suboptimal algorithms is reported. Several types of discrete sequences are modelled and the performance results are described. The genetic optimization algorithm behaves quite well in comparison to suboptimal approaches in terms of both performance and computational complexity.