The Kreiss constant K(A) of a stable matrix A conveys information about the transient behavior of system trajectories in response to initial conditions. We present an efficient way to compute the Kreiss constant K(A), and we show how feedback can be employed to make the Kreiss constant K(A(cl)) in closed loop significantly smaller. This is expected to reduce transients in the closed loop trajectories. The proposed method is compared to potential competing techniques.