This note presents a new design methodology that allows for flexible management of the tradeoff between the ability of a system to attenuate disturbance signals versus its expected worst peak-to-peak amplification. The proposed strategy applies to linear time-invariant systems which are subject to persistent disturbance signals and combines a recently developed quasi-robust linear programming concept with a well-known l(1)-optimal controller synthesis approach. The benefit of the resulting technique is demonstrated using an example.