International agreements for the International Commission for the Conservation of Atlantic Tunas (ICCAT) convention area imply that Atlantic tuna stocks should be managed by strategies based on maximum sustainable yield (MSY); however, there is concern whether this will actually ensure sustainability with sufficiently high probability consis- tent with the principals of the precautionary approach. Therefore, the performance of MSY management strategies based on current assessment procedures was evaluated using a computer simulation framework. The framework includes the data col- lection, assessment, prediction, and management processes, as well as the implementation of management regulations. It therefore provides an integrated way to evaluate the relative importance of and the interactions between each component of the system with regard to the overall success of the management strategy. The study elucidates guidelines about assessment and management that are general enough to be applied to all tunas in the Atlantic Ocean. It does so by comparing different hypotheses about management and assessment for three stocks (North Atlantic albacore, Atlantic bigeye and East Atlantic skipjack), which are representative of the variety encountered (i.e. from data rich to poor and tropical to temperate waters) in ICCAT stocks. Management performance was especially sensitive to the carrying capacity of the stock. The type of proxy used for MSY was more important to the success of the procedure than the frequency of assessment or the number of indices used in the assessment. Whilst the procedure was successful at achieving the management objectives for albacore, it was only partially successful for bigeye and was too conservative for skipjack.