Generally, selection indices used for the selection of livestock are linear combinations of estimated breeding values (EBVs), with each EBV weighted according to its marginal or relative economic value. This approach can be extended to non linear combinations. In both cases knowledge of economic weights is required. When economic values are not known, one can determine the relative weights that lead to the desired genetic progress. This approach was taken by Simm and Dingwall (1989) when designing the lean index for British terminal sire breeds. A weighting of +3 for lean in the carcase and -1 for fat in the carcase leads to near-maximum increase in lean, while maintaining amount of fat. This index has been highly effective over the last decade (MLC, 2002) to the extent that in recent years breeders have expressed concerns that offspring from high index ram have insufficient fat cover at slaughter. The current study aims to design an index that is broadly similar to the lean index, but puts a penalty on animals with a genetic merit for low fat cover.