Selection for production and reproduction in South African Merino sheep is always combined with selection based on visual appraisal and will, in all probability, remain so for many years to come. Heritabilities for acceptability were estimated using a threshold model to analyse data from two parent Merino studs. Effects included in the analysis were sex, birth status, age of dam and year of birth. An acceptable animal was defined as one that was present in the stud at 18 months of age, implying that such an animal would either be retained or sold for breeding purposes. This provided one threshold and two classes (acceptable or not acceptable). Records from the two studs used comprised 3011 progeny of 31 sires and 6495 progeny of 70 sires. Error variance was taken as unity and heritability estimated as h2 = 4σ2s/ 1+ σ2s where σ2s is the sire variance. Heritability estimates were 0.210 and 0.448. The results suggest that selection improvement for acceptability is possible, and that breeding values for this trait should be supplied for AI sires.