We develop a dynamic model of a fishery which simultaneously incorporates random stock growth and costly capital adjustment. Numerical techniques are used to solve for the resource-rent-maximizing harvest and capital investment policies. Capital rigidities bring diminishing marginal returns to the current period harvest, and introduce an incentive to smooth the catch over time. With density dependent stock growth, however, catch smoothing increases stock variability resulting in reduced average yields. The optimal management policy balances the catch smoothing benefits against yield loss. We calibrate the model to the Alaskan pacific halibut fishery to demonstrate the main insights.