Industrial fishing has been identified as a cause for life history changes in many harvested stocks, mainly because of the intense fishing mortality and its size-selectivity. Because these changes are potentially evolutionary, we investigate evolutionarily stable life-histories and yield in an energy-allocation state-dependent model for Northeast Arctic cod Gadus morhua. We focus on the evolutionary effects of size-selective fishing because regulation of gear selectivity may be an efficient management tool. Trawling, which harvests fish above a certain size, leads to early maturation except when fishing is low and confined to mature fish. Gillnets, where small and large fish escape, lead to late maturation for low to moderate harvest rates, but when harvest rates increase maturation age suddenly drops. This is because bell-shaped selectivity has two size-refuges, for fish that are below and above the harvestable size-classes. Depending on the harvest rate it either pays to grow through the harvestable slot and mature above it, or mature small below it. Sustainable yield on the evolutionary time-scale is highest when fishing is done by trawling, but only for a small parameter region. Fishing with gillnets is better able to withstand life-history evolution, and maintains yield over a wider range of fishing intensities.