Background: In future Best Linear Unbiased Prediction (BLUP) evaluations of dairy cattle, genomic selection ofyoung sires will cause evaluation biases and loss of accuracy once the selected ones get progeny. [br/] Methods: To avoid such bias in the estimation of breeding values, we propose to include information on all genotyped bulls, including the culled ones, in BLUP evaluations. Estimated breeding values based on genomic information were converted into genomic pseudo-performances and then analyzed simultaneously with actual performances. Using simulations based on actual data from the French Holstein population, bias and accuracy ofBLUP evaluations were computed for young sires undergoing progeny testing or genomic pre-selection. For bulls pre-selected based on their genomic profile, three different types of information can be included in the BLUPevaluations: (1) data from pre-selected genotyped candidate bulls with actual performances on their daughters, (2)data from bulls with both actual and genomic pseudo-performances, or (3) data from all the genotyped candidateswith genomic pseudo-performances. The effects of different levels of heritability, genomic pre-selection intensityand accuracy of genomic evaluation were considered.[br/] Results: Including information from all the genotyped candidates, i.e. genomic pseudo-performances for bothselected and culled candidates, removed bias from genetic evaluation and increased accuracy. This approach waseffective regardless of the magnitude of the initial bias and as long as the accuracy of the genomic evaluationswas sufficiently high.[br/] Conclusions: The proposed method can be easily and quickly implemented in BLUP evaluations at the national level, although some improvement is necessary to more accurately propagate genomic information from genotyped to non-genotyped animals. In addition, it is a convenient method to combine direct genomic, phenotypic and pedigree-based information in a multiple-step procedure.