Abstract Background When introgression of undesired exogenous genetic material occurs in a population intended to remain pure, actions are necessary to recover the original background. It has been shown that genome-wide information can replace pedigree information for different objectives and is a valuable tool in the fields of genetic conservation and breeding. In this simulation study, molecular information provided by 50 000 SNP was used to minimise the molecular coancestry between individuals of an admixed population and the foreign individuals that originally introgressed a native population in order to remove the exogenous DNA. Results This management method, which detects the ‘purest’ individuals to be used as parents for the next generation, allowed recovery of the native genetic background to a great extent in all simulated scenarios. However, it also caused an increase in inbreeding larger than expected because of the lower number of individuals selected as parents and the higher coancestry between them. In scenarios involving several introgression events the method was more efficient than in those involving a single introgression event because part of the genetic information was mixed with the native genetic material for a shorter period. Conclusions Genome-wide information can be used to identify the purest individuals via the minimisation of molecular coancestry between individuals of the admixed and exogenous populations. Removal of the undesired genetic material is more efficient with a molecular-based approach than with a pedigree-based approach.