Penaeid trawls are poorly selective fishing gears; contributing towards approximately 27% of global marine fisheries discards. Various options are available for mitigating penaeid-trawl bycatch, including gear modifications such as ‘bycatch reduction devices’ (BRDs) or codend mesh-size regulations. A precursor to developing modifications is information about the key target and bycatch species in terms of their sizes and morphology. Here we describe the relationships between these characteristics for the southern Brazilian industrial penaeid-trawl fishery within a broader objective of proposing more selective trawl configurations. Catches were sampled during 37 tows. Fifty-two species were caught, including two loggerhead turtles, Caretta caretta, one green turtle, Chelonia mydas, as well as 61 individuals of seven ray species classified as Endangered or Critically Endangered. One penaeid (Pleoticus muelleri) and 11 teleosts were assessed for various morphological relationships. The data demonstrated that both the existing conventionally used 26 mm (stretched mesh opening; SMO) mesh and a legislated size of 30 mm SMO are too small. Using morphological relationships, we propose testing a minimum diamond-shaped mesh size of at least 35 mm and a square-mesh window in the top of the codend comprising at least 48 mm mesh. Such a configuration would probably retain penaeids and larger teleosts, but allow many small teleosts to escape. Anteriorly located grids are also required to reduce the bycatch of charismatic species like turtles and rays. Wide-scale use of such BRDs should considerably reduce bycatches and the ancillary impacts of regional penaeid-trawl fisheries.