This paper investigates stabilization of single-input nonlinear systems by switching between two separate nonlinear feedback controllers. The first, a pseudolinear controller, provides a region of attraction U-0 around the equilibrium manifold. The second controller is high gain, and is designed to drive the state originating in a (larger) set of initial conditions U-1 into U-0. When the state enters U-0, the control is switched from the high-gain control to the pseudolinear control. Simple analytic estimates of both U-0 and U-1 are given. The method is applied in simulation to an acrobot, and in simulation and experiment to a rotating inverted pendulum.