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International audience; Much effort has been recently put into identifying causative quantitative trait nucleotides (QTN) in animal breeding, aiming more accurate genomic prediction. Among the genomic methods available, single-step GBLUP (ssGBLUP) became the choice because of its simplicity and potentially higher accuracy. When QTN are known, they need to be properly weighted, so the accuracy can be maximized. The weighted ssGBLUP is still under development, and a proper weighing algorithm is needed. The objectives of this study were to investigate whether ssGBLUP is useful for genomic prediction when causative variants are known and to verify the impact of different SNP weighting in ssGBLUP compared to GBLUP. Analyses involved about 4M records for stature of 3M cows. Genotypes were available for 27k sires for a regular 54k chip (BovineSNP50; Illumina), and imputed with extra 17k sequence variants having largest effects, including causative variants affecting stature and 32 other traits. Direct genomic value (DGV) and genomic EBV (GEBV) were calculated using GBLUP and ssGBLUP with regular genomic relationship matrices (G). Later, G was weighted based on the squared value of SNP effects or with nonlinear A equations, which limits the changes in SNP weights. In GBLUP, the residuals were either homogeneous or heterogeneous. Reliability (R2) was assessed from forward prediction of DGV or GEBV for young sires with at least 10 daughters. The lowest to highest R2 for DGV were by GBLUP with homogeneous residuals, GBLUP with heterogeneous residuals, and extracted from ssGBLUP. SNP weighting by nonlinear A increased R2 by up to 1.7% with homogeneous residuals and by up to 0.2% with heterogeneous residuals, compared to unweighted GBLUP. Linear weighting reduced accuracy in GBLUP and had no effect in ssGBLUP. Overall, adding 17k causative variants increased accuracy up to 0.6% in GBLUP, but had no impact in ssGBLUP. Reliability for DGV extracted from ssGBLUP was at least 0.6% more accurate than any DGV from GBLUP. Linear weighting is not helpful with causative variants with small effect. Gains with SNP weighting in multistep (GBLUP or SNP BLUP) may be partly due to corrections in modeling issues associated with pseudo-observations.