Fillet yield (i.e. the proportion of edible muscle in a fish) is a key economic trait for species sold as fillets. Its genetic improvement is complicated by several of its characteristics 1) it is a ratio trait, 2) its numerator (fillet weight) and denominator (body weight) are strongly correlated (correlations in the range 0.89-0.99), 3) it offers little phenotypic variation and 4) it cannot be measured on alive breeding candidates. In a former study, we showed that it could be improved by selection, especially with three selection indices, fillet yield, residual fillet weight and a ratio-specific linear index. However, it is well known that the heritability of ratio traits does not permit a reliable prediction of genetic gains. As predictability of genetic gains is a key requirement to define breeding programs, we investigated how genetic gains in fillet yield could be predicted by the genetic parameters of fillet yield, of residual fillet weight and of the component traits of the linear index. To this end, we compared simulated genetic gains with those estimated by classical prediction methods. This was done using real sets of genetic parameters obtained in nine populations of rainbow trout, European sea bass, gilthead sea bream and common carp. We show that the genetic parameters of fillet yield cannot be used to reliably predict genetic gains in fillet yield. Conversely, selection index theory using a linear index, combining either fillet weight and body weight or fillet weight and waste weight, provides almost perfect prediction of gains. Still, it is highly sensitive to the precision of the genetic and phenotypic correlations estimates, which should not be rounded to less than three decimals for fillet weight and body weight, while two decimals are appropriate for fillet weight and waste weight. A simple, reasonably precise alternative to the linear index is the use of residual fillet weight (the residual of the regression of fillet weight on body weight) as a surrogate for fillet yield.