The Law of the Sea and regional and national laws and agreements require exploited populations or stocks to be managed so that they can produce maximum sustainable yields. However, exploitation level and stock status are unknown for most stocks because the data required for full stock assessments are missing. This study presents a new method [abundance maximum sustainable yields (AMSY)] that estimates relative population size when no catch data are available using time series of catch-per-unit-effort or other relative abundance indices as the main input. AMSY predictions for relative stock size were not significantly different from the “true” values when compared with simulated data. Also, they were not significantly different from relative stock size estimated by data-rich models in 88% of the comparisons within 140 real stocks. Application of AMSY to 38 data-poor stocks showed the suitability of the method and led to the first assessments for 23 species. Given the lack of catch data as input, AMSY estimates of exploitation come with wide margins of uncertainty, which may not be suitable for management. However, AMSY seems to be well suited for estimating productivity as well as relative stock size and may, therefore, aid in the management of data-poor stocks.