We studied different genetic models and evaluation systems to select against a genetic disease with additive, recessive or polygenic inheritance in genetic conservation schemes. When using optimum contribution selection with a restriction on the rate of inbreeding ($\Delta$F) to select against a disease allele, selection directly on DNA-genotypes is, as expected, the most efficient strategy. Selection for BLUP or segregation analysis breeding value estimates both need 1-2 generations more to halve the frequency of the disease allele, while these methods do not require knowledge of the disease mutation at the DNA level. BLUP and segregation analysis methods were equally efficient when selecting against a disease with single gene or complex polygene inheritance, i.e. knowledge about the mode of inheritance of the disease was not needed for efficient selection against the disease. Smaller schemes or schemes with a more stringent restriction on $\Delta$F needed more generations to halve the frequency of the disease alleles or the fraction of diseased animals. Optimum contribution selection maintained $\Delta$F at its predefined level, even when selection of females was at random. It is argued that in the investigated small conservation schemes with selection against a genetic defect, control of $\Delta$F is very important.