Simple models that can forecast yield loss from weed seedling density at crop emergence are useful tools for both research and practice. In 1985 Cousens presented the rectangular hyperbolic curve as a solution to this problem for the one-weed species case (Cousens 1985a). To address the multi-weed species case, the present theoretical paper investigates two published models and develops a third model, termed ‘recursive density equivalents’. The models were analysed and evaluated based on their biological rationale and using already published data. The earlier models were both found to rely on biologically unrealistic assumptions. The new model avoided additional assumptions, providing a neutral method of summarizing the Cousens curves for many species. Recursive density equivalents were found to be additive in a more intuitive fashion than the ‘density equivalents’ introduced earlier. An over-estimation bias was found to be inherent in the earlier density equivalents model, increasing with species richness. The new model corrected for this bias when checked against one year's field data but for another year, both models over-estimated markedly. All three models were found to be too simple to accommodate all possible modes of intra- and inter-specific competition, yet the new model is an improvement, as it agrees better with the biological principles of crop-weed competition.