A laser diode subject to a phase-conjugate optical feedback can exhibit rich nonlinear dynamics and chaos. We report here on two bifurcation mechanisms that appear when increasing the amount of light being fed back to the laser. First, we report on a full suppression of chaos from a crisis induced by a saddle-node bifurcation on self-pulsing, so-called external-cavity-mode solutions (ECMs). Second, the feedback-dependent torus and saddle-node bifurcations on ECMs may be responsible for large regions of bistability between ECMs of different and high (beyond gigahertz) frequencies.