Generalized H-infinity loopshaping is developed for a particular weighted mixed sensitivity minimization task, A Free parameter is introduced to tradeoff minimizations of sensitivity and complementary sensitivity in the H-infinity performance index. A quadratically convergent algorithm is derived fur computing the optimal performance index, and a state-space solution is obtained for suboptimal controllers. These results are applicable to stabilization of uncertain systems where normalized coprime Factors involve parametrically weighted H-infinity norm-bounded perturbations. Controller reduction is also investigated for the parametric H-infinity loopshaping. Robust stability condition for using the reduced-order controller is established, and an estimate for the associated H-infinity, performance is obtained. Similar results are derived for normalized linear quadratic Gaussian (LQG) control.