In this paper an alternative method for designing optimal H₂/H_∞ dynamic output-feedback controllers is presented. The design occurs in two phases. In the first one, a suboptimal, mixed-objective, dynamic output-feedback controller is synthesized, by one of the available methods. This controller is suboptimal in the sense that it uses the same Lyapunov matrix in both constraints, thus introduces some conservatism in the solution. This controller constitutes then the initial step of the computation of an optimal H₂/H_∞ dynamic output-feedback controller, computation which represents the second phase of the design process. The path-following method used in this phase to convert to linear matrix inequalities (LMI's) the bilinear matrix inequalities (BMI's), which appear typically in this design, makes it possible to use two different Lyapunov matrices in the two objective constraints, thus reducing the conservatism mentioned previously.