We consider the optimal reinsurance problem from the point of view of a direct insurer owning several dependent risks, assuming a maximal expected utility criterion, and the independent negotiation of reinsurance for each risk. Without any particular hypothesis on the dependency structure, we show that optimal treaties exist in a class of independent randomized contracts. We derive optimality conditions and show that under mild assumptions, the optimal contracts are of a classical (non-randomized) type. A specific form of the optimality conditions applies in that case. We present a numerical scheme to solve the optimality conditions.