QTL detection using the regression of phenotypes on transmission probability is largely used when large families are available. In three generations designs, the use of a ‘de-regressed proof’ as a phenotype to be analysed was proposed by Weller et al. (1990) and Tribout et al. (2008).Our work generalizes this approach. A score (that we define as a ‘generalized de-regressed proof’) is described, which combines performance phenotypes recorded in multigenerational offspring of genotyped individuals. Estimation of the QTL effect on this score with a simple regression is unbiased. The link between this score and the BLUP animal model of the polygenic effect is demonstrated. The theory is developed and two simple examples illustrate how this technique can be implemented.