Devices for laser welding using welding wire have a welding head, a wire guide for the welding wire, and a wire feed drive. The welding wire can be moved by the wire feed drive during a welding process with a feed movement in a feed direction, guided by the wire guide. A positioning device has a positioning drive, by which the welding wire is moved in an oscillating manner in the longitudinal direction of the welding wire, when a wire end of the welding wire is arranged in a welding readiness position. Methods for laser welding using a welding wire as added material are carried out using the devices. A control program controls the devices. The devices for laser welding can be provided as a part of a welding robot.