ABSTRACT In single-step analyses, missing genotypes are explicitly or implicitly imputed, and this requires centering the observed genotypes, ideally using the mean of the unselected founders. If genotypes are only available on selected individuals, centering on the unselected founder mean is impossible. Here, computer simulation is used to study an alternative analysis that does not require centering genotypes but fits the mean μg of unselected individuals as a fixed effect. To improve numerical properties of the analysis, centering the entire matrix of observed and imputed genotypes, using their sample means can be done in addition to fitting μg. Starting with observed diplotypes from 721 cattle, a 5 generation population was simulated with sire selection to produce 40,000 individuals with phenotypes of which the 1,000 sires had genotypes. The next generation of 8,000 genotyped individuals was used for validation. Evaluations were undertaken: with (J) or without (N) μg when marker covariates were not centered; and with (JC) or without (C) μg when all marker covariates were centered. A pedigree based evaluation was less accurate than genomic analyses. Centering did not influence accuracy of genomic prediction, but fitting μg did. Accuracies were improved when the panel comprised only QTL, models JC and J had accuracies of 99.2%; and models C and N had accuracies of 85.6%. When only markers were in the panel, the 4 models had accuracies of 63.9%. In panels that included causal variants, fitting μg in the model improved accuracy, but had little impact when the panel contained only markers.