Current scientific management objectives for ICES roundfish stocks are to ensure conservation of the biological resource and do not explicitly consider economic or social objectives. For example, there are currently no objectives to maximize the sustainable yield or to reduce variability in total allowable catches (TACs). This is despite the fact that the current system can result in wide annual fluctuations in TAC, limiting the ability of the fishing industry to plan for the future. Therefore, this study evaluated management strategies that stabilized catches by setting bounds on the interannual variability in TACs. An integrated modelling framework was used, which simulated both the real and observed systems and the interactions between system components. This allowed the evaluation of candidate management strategies with respect to the intrinsic properties of the systems, as well as our ability to observe, monitor, assess, and control them. Strategies were evaluated in terms of risk (measured as the probability of spawning-stock biomass falling below a biomass threshold for the stock) and cumulative yield. In general, bounds on interannual TAC change of 10% and 20% affected the ability to achieve management targets, although the outcome of applying TAC bounds could not have been pre-judged because results were highly dependent on the specific biology of the stock, current status, and the interaction with assessment and management. For example, for North Sea haddock, management became less responsive to fluctuations resulting from large recruitment events. Simulated target fishing mortality levels were rarely achieved, regardless of the TAC bound applied, and actual fishing mortality rates oscillated around the target. In the longer term, more restrictive bounds resulted in oscillations of greater amplitude and wavelength in yield and SSB. Bounds had less effect when a stock was close to the biomass corresponding to the target F. Risk for stocks that are declining or currently at low abundance may be greater, because if bounds restrict the extent to which TACs can be reduced each year, they could lead to collapse of the stock and the loss of all future revenue. However, for a recovered stock or one at high abundance, the loss of yield as a result of bounds would be smaller than that caused by the total collapse of the fishery. At low stock size or if the stock was declining, catches should be changed more rapidly than when the stock was increasing or at a high level, especially high stock sizes acting as an insurance against uncertainty. Therefore, rebuilding strategies, and strategies aimed at maintaining the stock above prescribed limits, should be considered separately.