Mixed objective control problems have attracted much attention lately since they allow for capturing different performance specifications. However, optimal multiobjective controllers may exhibit some undesirable properties such as arbitrarily high order. This paper addresses the problem of designing stabilizing controllers that minimize an upper bound of the l(1) norm of a certain closed-loop transfer function, while maintaining the H-2 norm (mixed l(1)/H-2), or the H-infinity norm (mixed l(1)/H-infinity), of a different transfer function below a prespecified level. The main results show that these suboptimal controllers have the same order as the generalized plant and can be synthesized by a two-stage process, involving an LMI optimization problem and a line search over (0, 1).