A reflector lamp (1) comprising a reflector (2) having an opening (6) opposite to a light emission window (7), an electric lamp (10) comprising a closed lamp vessel (11) positioned with an end portion (16) in the lamp opening of the reflector, an electric element (13) arranged on the optical axis (4) in the lamp vessel, and a support body (20). The support body comprises reflector fastening means (22) for fastening the support body to the reflector, and lamp fastening means (21) for fastening the support body to the end portion of the lamp vessel. Viewed in a direction from the lamp opening along the optical axis towards the light emission window, the support body is fastened to the reflector solely at a location beyond the lamp opening of the reflector.