Single-step genomic BLUP (ssGBLUP) is the method of choice for genomic evaluation because of simplicity and ability to combine pedigree, genotypes, and phenotypes. As the availability of sequence data is increasing, we investigated whether ssGBLUP can be useful for genomic analyses when causative Quantitative Trait Nucleotide (QTN) are known. Simulations included 180k animals from 11 generations. Phenotypes (h2=0.3) were available for all animals in generations 6-10. A total of 24k parents in generations 6-10 and 5k validation animals in generation 11 were genotyped for 60k SNP. The genetic variance was fully accounted for by 100 or 1000 biallelic QTN. Genomic relationship matrices were computed based on: unweighted 60k SNP; unweighted 60k SNP and QTN; 60k SNP and QTN with variance from GWAS; unweighted 60k SNP and QTN with known variance; only QTN. Accuracy of EBV for validation animals were computed by BLUP and ssGBLUP. To ensure full rank, the genomic relationship matrix (G) was blended with 1% or 5% of the numerator relationship matrix. The inverse of G was computed directly or using APY, the algorithm that exploits the limited dimensionality of G for sparse computations. This dimensionality was calculated as the number of largest eigenvalues explaining 98% of the variance of G. Rank of G with 100 QTN was 16,980 for G based on unweighted 60k SNP; 19,112 after 5% blending; 5,093 for G with 60k SNP and QTN with known variance; 98 when only QTN were used to create G. With 1000 QTN, trends were similar, but the rank with only QTN was 930. BLUP accuracy for validation animals was 0.32. Accuracies increased to 0.49, 0.53, 0.63, and 0.89 for ssGBLUP with unweighted 60k SNP, unweighted 60k SNP and QTN, 60k SNP and QTN with variance from GWAS, and unweighted 60k SNP and QTN with known variance, respectively. When G was constructed based only on QTN, the accuracy was 0.95 with 5% blending and 0.99 with 1% blending. Accuracies with 1000 QTN were lower, with a similar trend. Accuracies using APY G-1 were equal or higher than those with direct inverse. Single-step genomic BLUP can account for causative variants with nearly optimum accuracy when QTN and their variances are known.