In a personal headlamp, a housing, containing both an illumination source and a power source, is mounted in cantilever fashion on a bracket that comprises a back part and a collar fastened to, and extending forward from, the back part. A resilient pawl, which extends from the back part through a slot in the collar, is engageable with any selected one of a series of circumferentially spaced notches formed on a ring-like protrusion on the housing that fits rotatably into the collar.