Genomic imprinting is a term applied to an epigenetic phenomenon where alleles are fully or partially inactivated depending on their parental origin. The relevance of this kind of parent-of-origin effects (POEs) for agriculturally important traits is widely known. A model (imprinting model) with a transmitting ability (TA) as sire and a TA as dam has been proposed that provides an estimate of the imprinting variance, whether the allelic inactivation is maternal, paternal, full or partial. Although the model can be used in a reduced version, large data sets still prevent the imprinting variance from being estimated. To further reduce the size of the equation system, we developed a parsimonious imprinting model with genetic effects for male ancestors only, as the TA as dam is replaced by her father’s TA. This parsimonious model was applied to 1 366 160 Simmental fattening bulls with slaughter data available on killing out percentage, net BW gain, EUROP class and fat score in a linear and generalised linear version. The pedigrees contained up to 2 637 761 ancestors. Proportion of the total genetic variance attributed to POEs ranged between 8.6% and 17.0%. On average, the maternal gamete accounted for the greater proportion of the imprinting variance. An equivalent version of the parsimonious model facilitated the estimation of POEs with reliabilities ranging between zero and 0.97.