This paper presents a simulation which evaluates the performance of alternative selection index configurations in the context of a breeding program where traits with non-linear economic value are approaching an economic optimum. The simulation described uses a simple population structure that approximately mimics selection in dual purpose flocks in New Zealand, where number of lambs born is believed to be approaching an optimum, while other genetically correlated traits with linear economic values are assumed to not be approaching any economic optimum. A “non-linear below the optimum and then flat” approach to index formulation was found to be at least comparable in efficiency to the approach of regularly updating the linear index with short (15 year) and long (greater than 30 year) time frames, especially when the current average value of the “non-linear” trait is at a reasonable distance from the optimum. Use of a non-linear index that is efficient may have other benefits in highly heterogeneous industries (breeds and production environments) such as the New Zealand sheep industry.