A number of techniques have been developed in recent years for the analysis and design of controllers which are robust with respect to structured complex uncertainty. In particular the complex mu synthesis procedure has been successfully applied to a number of engineering problems. However, the presence of real parametric uncertainty in the problem substantially complicates matters, so that standard complex mu synthesis techniques are no longer adequate. This paper develops a procedure to tackle the mixed (real and complex) mu synthesis problem. This procedure involves a (D, G)-K iteration between computing the mixed mu upper bound and solving an H-infinity optimal control problem. The resulting scheme has guaranteed convergence, though not necessarily to the global optimum of the (non-convex) problem. The (D, G)-K iteration has been implemented in software, and several controller designs are carried out and compared with the corresponding complex mu synthesis designs, to illustrate the advantages of the new technique.