For a variety of reasons, it is not always easy for fishery managers to control fishing catch and/or effort using first-best policy instruments. As a result, so-called buy-back programmes which effectively restrict the use of selected inputs to the production of fishing effort are a common policy instrument in many fisheries around the world. In this paper, we investigate two issues, one being t h e determinants of the efficiency of buy-back programmes and the other being the "optimal" (i.e. second best) level of buy-back under different circumstances. Overall efficiency of a buy-back programme depends firstly on the efficacy of a reduction in level of use of selected fishing inputs on the level of fishing effort applied to the fish stock , and secondly on the extent to which total cost of fishing effort under a buy-back programme exceeds the minimum total cost necessary to generate the same level of effort in an unrestricted fishery. The elasticity of supply of effort given restricted use of selected inputs is shown to be the critical determinant of both of the above aspects. This elasticity varies directly with the elasticity of substitution between restricted and unrestricted inputs to fishing effort, and inversely with the share of total cost of fishing effort accounted for by inputs subject to the buy-back programme. For particular cases investigated in the paper, this elasticity is affected by the intensity of exploitation of the fish stock. We conclude that a buy-back programme is likely to be close to first-best as long as non-restricted inputs cannot easily be substituted for restricted inputs and/or as long as restricted inputs account for a large proportion of total factor cost. Our results also suggest that efficiency of a buy-back programme will be higher if the economic pressure to exploit the fish stock intensively is not too great. When these conditions are not present, buy-back programmes are likely to be a relatively inefficient policy instrument for generating a net social surplus for society.