The genetic and economic efficiency of alternative selection schemes and breeding objectives for the Karagouniki dairy sheep in Greece was investigated by model calculations. Criteria of efficiency were the annual genetic gain for the aggregate breeding value, the profit per ewe in the population and the annual selection responses for single traits. The introduction of a two-tier selection scheme, where the recorded ewes are separated into a nucleus and a pre-nucleus, was found superior in both genetic and economic terms for a breeding objective comprising the traits milk yield and number of lambs weaned per ewe per annum. Highest rates for annual genetic gain and selection responses were obtained when the nucleus size was proportionately 0·05 of the population (200 000 ewes), the size of the test matings 0·50 to 0·60 of the size of the pre-nucleus unit (0·10 of the population) and the number of daughters per test ram 40. Opening the nucleus to replacement ewes from the lower tier did not affect positively the annual genetic gain and the selection responses. Furthermore, a breeding objective comprising the traits fat yield and number of lambs weaned per ewe and per annum was found very efficient in both genetic and economic terms while selection on growth and carcass traits did not seem to be justified.