The mode-hop behavior and the power characteristics of a laser diode with wavelength-selective optical feedback are experimentally investigated. The feedback is provided by external volume holographic gratings, also called ‘Bragg mirrors’, at normal incidence. We demonstrate that a Bragg mirror forces a laser diode to operate only within a narrow wavelength range, and that the emission wavelength of the laser diode is stabilized against variations of the injection current. Moreover, we present periodic undulations of the power characteristics of the laser, depending on the driving current. They can be qualitatively explained with a simple model which takes into account that the threshold gain in the laser system strongly depends on the wavelength.