This paper studies a high-gain observer with a nonlinear gain. The nonlinearity is chosen to have a higher observer gain during the transient period and a lower gain afterwards, thus overcoming the tradeoff between fast state reconstruction and measurement noise attenuation. The observer is designed such that the behavior of the innovation process can be controlled separately from the other system states. This is accomplished by assigning one fast eigenvalue, with the remaining eigenvalues chosen relatively slow. Without this key step, the stability analysis for the proposed observer is unattainable. Recently, a switched observer approach has been investigated, but the nonlinear gain approach bypasses the complications associated with switching, with little to no appreciable degradation in performance. This paper presents a new model for the nonlinear observer, accompanied by a discussion focusing on the main ideas behind the proof.