The debate about the statistics of DNA profiling in forensic science casework has been carried out mainly from the perspective which is generally known as "match/binning." This approach has an initial appeal because of its apparent conceptual simplicity. However, the simplicity is illusory because it encourages misconceptions which obscure the essential forensic issues. This is exemplified in a recent report of the National Research Council, which places great emphasis on the need for conservative estimation of relative frequencies while missing the point that the power of RFLP technology cannot be realized if the matching stage is inefficient. Our approach to the problem is a one-stage rather than a two-stage process, by means of one function--the likelihood ratio--which determines the evidential strength. This paper describes experiments which have been carried out to assess the power of the method in forensic science and compares it with match/binning methodology. Tests for gauging the effects of between-probe dependence are included, with the results complementing those of Risch and Devlin.