Two experiments were conducted in an Australian penaeid stow-net fishery to: (i) validate the use of a fine-meshed cover for determining the selectivity of codends, and (ii) use this cover to quantify and compare the selectivity of a conventional 30-mm diamond-mesh codend and two new square-mesh designs made from 20- and 30-mm mesh, hung on the bar. In the first experiment the codend cover had minimal impact on the fishing performance of the stow net. The 30-mm square-mesh codend tested during the second experiment significantly improved the selectivity of the stow net, measured as an increase in school prawn (Metapenaeus macleayi Haswell, 1879) carapace length at 50% probability of retention (L), and a reduction in the unwanted bycatches of juvenile eastern king prawns (Penaeus plebejus Hess, 1865) and small, non-commercial fish. However, a concomitant increase in selection range (SR) indicated that unacceptable quantities of target-sized school prawns escaped. In contrast, the 20-mm square- and 30-mm diamond-mesh codends were virtually non-selective for the sizes of school prawns encountering the gear. Compared to the 30-mm diamond-mesh codend, the 20-mm square-mesh codend did, however, reduce the quantities of eastern king prawns and non-penaeid bycatch retained. The results are attributed to the geometries of the codends tested and provide directions for future research into modifications to improve the selectivity of stow nets.