Russell and Burch's Three Rs principle of replacement, reduction and refinement offers a useful concept for the scientific and ethical evaluation of the use of animals in scientific procedures. Replacement, reduction and refinement are often considered separately, but when applied, one of the Three Rs may have a positive or negative effect on one or both of the other Rs. This paper explores the interplay between the Three Rs and provides examples where the Three Rs have a positive interaction and where they are in conflict with each other. For example, all Three Rs positively interact in the use of cell cultures, but validation studies of replacement techniques may initially increase the numbers of animals used; therefore replacement and reduction are in conflict. Several models of cost-benefit analyses, used by animal ethics committees to justify or reject animal experimentation, contain elements such as quality and significance of the research, the credibility of the research group and the discomfort caused to the animals. Although these models consider the Three Rs, each R is considered independently of the others. Consequently, moral dilemmas may arise when reviewing proposals in which the Three Rs conflict. Currently there is no legal guidance relating to the prioritisation of the Three Rs, but guidance is required to facilitate their use. For example, does a significant reduction in animal numbers justify increased individual suffering? Moral justifications deserve more attention when considering the Three Rs in general, and when considering the application of one or more Rs to a procedure, to a protocol, or to the wider research programme.