An optimum way of selecting animals is through a prediction of their genetic merit (estimated breeding value, EBV), which can be achieved using a best linear unbiased predictor (BLUP) (Henderson, 1975). Selection decisions in a commercial environment, however, are rarely made solely on genetic merit but also on additional factors, an important example of which is to limit the accumulation of inbreeding. Comparison of rates of inbreeding under BLUP for a range of hentabilities highlights a trend of increasing inbreeding with decreasing heritability. It is therefore proposed that selection using a heritability which is artificially raised would yield lower rates of inbreeding than would otherwise be the case.