In this paper, we take a new look at the mixed structured singular value problem, a problem of finding important applications in robust stability analysis. Several new upper bounds are proposed using a very simple approach which we call the multiplier approach. These new bounds are convex and computable by using linear matrix inequality (LMI) techniques. We show, most importantly, that these upper bounds are actually lower bounds of a well-known upper bound which involves the so-called D-scaling (for complex perturbations) and G-scaling (for real perturbations).