This paper introduces a new approach for output feedback stabilization of SISO systems which, unlike most of the techniques found in the literature, does not use high-gain observers and control input saturation to achieve separation between the state feedback and observer designs. Rather, we show that by using nonlinear observers, together with a projection algorithm, the same kind of separation principle is achieved for a larger class of systems, namely stabilizable and incompletely observable plants. Furthermore, this new approach avoids using knowledge of the inverse of the observability mapping, which is needed by most techniques in the literature when controlling general stabilizable systems.