We outline a procedure by which conservative management (defined as management which errs on the side of the resources in the face of uncertainty) can use a series of stepwise analyses to explore for possible overfishing in multispecies fisheries for which there is only aggregated data on effort. The procedure provides a multivariate framework for analyzing these data and has two statistical aspects. The first aspect develops a formula for the 95% confidence intervals around the predicted MSY estimate. The second aspect fits a seemingly unrelated regression (SUR) model which takes into consideration the possibility of correlation among the individual species' catch data. We apply this procedure to the multispecies pelagic fisheries from West Africa. Our philosophy is not to advocate the use of these models to manage a fishery, but to advocate a conservative approach to those fisheries for which only such minimal data exist. Our analyses denote the comparative broad 95% confidence intervals about MSY estimates and that the SUR is applicable for this multispecies fishery. Our surplus production fits suggest overfishing in one of the six single species fits and in both of the two single genius aggregations. While the fit of the aggregate total catch doesn't suggest overfishing, it does suggest that the fishery is almost at FMSY. We conclude that these fits provide management with a more realistic approach to the status of the stocks than a previously published equilibrium fit, which suggested a tremendous potential for increasing catch by increasing effort outside of the historic range.