We study a repairable system with Markovian deterioration and partial repair options, carried out at fixed times $n=1,2,\ldots$ and look for optimal strategies under certain conditions. Two optimality criteria are considered: expected discounted cost and long-run average cost. Douer and Yechiali found conditions under which a policy in the class of generalized control limit policies is optimal. In this paper conditions are found under which an optimal policy is a control-limit policy. We explicitly explain how to derive this optimal policy; numerical examples are given, too.