In this paper we consider an L2 control problem with an Linfinity norm on the closed-loop impulse response. To do this we first construct an upper bound for the Linfinity norm of the impulse response of the closed-loop system. To perform controller synthesis, we then modify the standard LQG cost functional by including an additional penalty term that weights the Linfinity norm of the impulse response of the closed-loop system. A numerical example is given to illustrate the improved Linfinity response of the closed-loop system.