The discussion focuses on a number of differences that have been identified and used to argue for or against each method. The two issues regarding RMNE are whether it returns a statistic that cannot be interpreted directly in the context of a court case, as well as whether it wastes information and hence is less powerful. One issue discussed regarding LRs is whether they are complex and difficult to phrase, and another issue is whether LRs assume a number of contributors, an assumption that cannot be justified. A third issue regarding LRs is whether they require the development of hypotheses that may be difficult and that may change. A fourth LR issue discussed is whether there are mixtures that are too complex for the LR method to interpret. After analyzing each of these issues, the paper concludes that only two of the adverse claims against LRs and RMNE have force: LRs are more difficult to present in court; and the RMNE statistic wastes information that should be used. The RMNE methods seek to determine the fraction of the population that would not be excluded as a contributor to the crime-scene stain. Typical applications of the LR method assume a number of contributors to the mixture and make use of the profiles of persons who can be safely assumed to be in the mixture (conditioning profiles) and always make use of the genotype of the profile of interest (usually the suspect). 18 references and appended details of the RMNE calculation