Conservation programmes aim at minimising the loss of genetic diversity, which allows populations to adapt to potential environmental changes. This can be achieved by calculating how many offspring every individual should contribute to the next generation to minimise global coancestry. However, an undesired consequence of this strategy is that it maintains deleterious mutations, compromising the viability of the population. In order to avoid this, optimal contributions could be combined with inbred matings, to expose and eliminate recessive deleterious mutations by natural selection in a process known as purging. Although some populations that have undergone purging experienced reduced inbreeding depression, this effect is not consistent across species. Whether purging by inbred matings is efficient in conservation programmes depends on the balance between the loss of diversity, the initial decrease in fitness and the reduction in mutational load. Here we perform computer simulations to determine whether managing a population by combining optimal contributions with inbred matings improves its long-term viability while keeping reasonable levels of diversity. We compare the management based on genealogical information with management based on molecular data to calculate coancestries. In the scenarios analysed, inbred matings never led to higher fitness and usually maintained lower diversity than random or minimum coancestry matings. Replacing genealogical with molecular coancestry can maintain a larger genetic diversity but can also lead to a lower fitness. Our results are strongly dependent on the mutational model assumed for the trait under selection, the population size during management and the reproductive rate.