Mathematical analysis and computer simulations are used to evaluate three modifications to Kauffman's NK model in an attempt to incorporate unexplored aspects of epistatic interaction between loci in genome evolution. Two modifications - one to the amount and the other to the distribution of epistatic interaction - further support Kauffman's conclusion that high levels of epistatic interaction lead to a decrease in overall fitness of the genome. The third model, however, provides a condition under which increased epistatic interaction at certain loci results in higher genome fitness.