Substitutive (replacement) and partial additive experimental designs, with their underlying models, remain the two most popular techniques in weed-crop competition studies, despite considerable criticism of these approaches in the recent literature. We review standard designs for two-species competition experiments and demonstrate the advantages of a reciprocal yield model applied to data from an additive series experiment, using mixtures of Japanese millet and tomato. A traditional replacement series analysis failed to provide a general model of competition among these two species over several total plant densities, while an application of a reciprocal yield (inverse linear) model to the same data was successful. This technique allows evaluation of the influences of both weed on crop and crop on weed, as well as the partitioning of net competition effects into intra- and interspecific components. One Japanese millet plant was competitively equivalent to 3.7 tomato plants, as measured by effects on tomato biomass, while one tomato plant was equivalent to 0.14 Japanese millet plants, as measured by effects on millet biomass. Skewness of per plant biomass distribution is shown to be a result but not an unambiguous measure of competition. Expansion of a reciprocal yield model to mixtures of more than two species is illustrated using three species of duckweed. While some caution is recommended, the reciprocal yield analysis applied to data from appropriately designed experiments is a substantial improvement over more traditional methods.