The two phase method is a well-known method to find Pareto optimal solutions to biobjective combinatorial optimization problems [Ulungu and Teghem, 95]. We adapt this method to Lorenz dominance, a model proposed in economics to refine Pareto dominance by focusing on well-balanced solutions. This adaptation amounts to computing the solutions that optimize an OWA aggregator [Yager, 98] in a first phase, and all the remaining Lorenz optimal solutions in a second phase. We present the results obtained for different biobjective combinatorial optimization problems.