The authors describe the optically bistable operation of an all-optical nonlinear Fabry-Perot etalon (NLFP) in which the power-dependent cavity phase shift has a contribution dependent on the power incident on the cavity. When the contributions have the same parity, the optically-bistable behavior is essentially the same as that seen in the now standard bistable NLFP (counterclockwise hysteresis in transmission). For opposite parity there is a range of relative strengths for which bistable operation cannot be obtained, but, outside of that range, bistable behavior having clockwise hysteresis in transmission is possible. This latter bistable behavior is demonstrated, with the NLFP being a GaAlAs laser diode amplifier driven by a similar diode laser. Low-frequency modulation of the laser power by direct variation of the laser drive current produced a small shift in laser wavelength proportional to the laser power, providing the cavity phase shift term proportional to the incident power, while the nonlinear refractive index of the NLFP provided the phase shift proportional to the transmitted power. >