We present a new method called the natural decay of mixing (NDM) method for introducing decoherence effects into the semiclassical Ehrenfest self-consistent potential method. The NDM method is similar in spirit to two recently developed methods, the continuous surface switching (CSS) and continuous surface switching II (CSS2) methods, but, like the pure semiclassical Ehrenfest method, it involves only a single variable that serves as both the weight of an electronic state and its electronic population. We demonstrate how this allows the NDM method to be applied to systems where the CSS and CSS2 methods cannot be applied, and also to cases where the CSS and CSS2 methods would be prohibitively expensive. The method is tested for electronically nonadiabatic processes, both reactive and nonreactive, and in a wider context it contributes to the rapidly blossoming fields of quantum measurement and hybrid quantum/classical algorithms for the dynamics of complex systems.