The expected change in fitness under inbreeding due to deleterious recessive alleles depends on the amount of inbreeding load harbored by a population, that is, the load of deleterious recessive mutations concealed in the heterozygous state, and the opposing effect of genetic purging to remove such a load. This change in fitness can be thus predicted if an estimate of the inbreeding load and the purging coefficient (the parameter that quantifies the amount of purging) are available. These two parameters can be estimated in pedigreed populations, as has been shown for populations under random mating. A question arises whether these parameters can also be estimated under other breeding systems as well as whether they allow accurate prediction of the corresponding expected change in fitness. In conservation programs, it is usually recommended to preserve genetic diversity by equalizing contributions from parents to progeny and avoiding inbred matings. Regular systems of inbreeding have also been proposed as breeding conservation strategies to purge the inbreeding load. Using computer simulations, we first test a method to jointly estimate the initial inbreeding load and the purging coefficient in populations subjected to equalization of parental contributions, circular mating, and partial full-sib mating. Then, using the expected values of the inbreeding coefficient and the variance of family size, as well as the estimates of the inbreeding load and the purging coefficient, we make simple predictions of the change in fitness over generations under these breeding systems and compare them with simulation results. We discuss how these fitness predictions can help undertaking conservation designs under different breeding scenarios.