After the introduction of the new tobacco regime, many regions in Greece, formerly specialized in tobacco cultivation, are now facing serious threats of economic and social decline. Sheep farming is considered by many analysts as a viable alternative to tobacco. This study analyses the financial performance of sheep production and the risk that producers are taking. Through a stochastic efficiency analysis with respect to a function we explore the economic viability of conventional and organic sheep farming; key factors determining the economic outcome of these activities are also investigated. Both organic and conventional sheep farming appear as viable alternatives. The viability of organic farming lies, mainly, in organic payments. Conventional farming generates a slightly lower but less uncertain net return.