Current practices for computing maximum sustainable yield (MSY) from fisheries result in yields that are rarely maximized and never sustainable. We recast MSY determination as the maximization of constant catch, which is subject to the risk of stock depletion below levels necessary to generate the target constant catch. Monte Carlo yield models with stochastic recruitment functions were used to examine the effects of constant-catch policies on fishing mortality, catch, and stock size. Three additional output variables and their statistical properties were developed as indices of fishery variability and risk: delta catch, the change in catch between successive years; length of run, the number of successive years the target constant catch was attained; and the proportion of years in which the target constant catch was not taken. We constructed two stochastic yield models to account for different stock-recruitment relationships. The first used a statistical distribution of recruitment values in which recruitment was independent of spawning-stock biomass; the second used a stochastic form of the Shepherd stock-recruitment relationship. For the parametric stock-recruitment model, the ability to sustain moderate yields was critically dependent on rehabilitation strategies for years when total stock size dropped below that necessary to support the constant-catch target. Depending on specific stock dynamics, fluctuations in annual yields can be damped by accumulating harvestable stock and setting constant-catch targets that, on average, result in low to moderate fishing mortality. Target constant catches thus defined represent a stochastic analog of MSY and estimate the long-term potential catch from the stock. The desirability of such strategies is determined by the relative value of averting the risk of undesirable stock and catch fluctuations versus the costs of foregone yields due to natural mortality and density-dependent processes.