Selection indices for terminal sire sheep breeds were examined. The selection goal comprised carcass lean and fat weight at 150 days of age, and index measurements examined were live weight (LW), ultrasonic fat depth (UFD) and ultrasonic muscle depth (UMD) at 150 days of age. Relative economic values (REV) for lean weight ranged from + 1 to +5 at an REV of -1 for fat weight. Literature or unpublished estimates of phenotypic and genetic parameters were used. The expected annual responses to selection on different indices were calculated, assuming an average ratio of selection intensity:generation interval, for the two sexes, of 0.60. Responses ranged from +16 g lean, -222 g fat year-1 (REVS +1:-1) to +211 g lean, +132 g fat year-1 (REVS +5:-1). The theoretical maximum responses were also calculated, assuming perfect precision of predicting carcass composition. These ranged from + 107 g lean, - 270 g fat year-1 (REVS + 1: -1) to + 282 g lean, +57 g fat year-1 (REVS +5:-1). Further increases in the response in lean weight of 4-39 g year-1 were expected from selection on indices including measurements on half-sibs. REVS of +3 and -1 for the index based on LW, UFD and UMD were thought to be most appropriate, since the expected response in lean weight was approaching its maximum value, whilst the increase in fat was still relatively small. Expected responses in lean and fat weight were 94 and 26% of those expected from selection on LW alone. With perfect precision of prediction up to 90 g year-1 extra lean weight could be achieved, with a reduction in fat weight at 150 days of age. The index with REVS of +3 and -1 is being used to select performance-tested rams in the Edinburgh School of Agriculture Suffolk flock.