A method of joining an electrically-conductive elongate member, which may be a multi-strand cable, to an electrically-conductive electrode, possibly for an implantable medical device, requires that the free end of the electrically-conductive member be inserted axially into a longitudinally extending passage of a tubular crimp/weld sleeve. Thereupon, the crimp/weld sleeve is crimped onto the electrically-conductive elongate member to achieve firm engagement between the crimp/weld sleeve and the electrically-conductive elongate member. The crimp/weld sleeve is provided with a radially outward extending prominent member which may be one of a variety of shapes. The electrode is tubular, overlies the outer surface of a longitudinally extending lead body, and is formed with an aperture defined by a rim having a transverse dimension greater than the transverse dimension of the prominent member. The crimp/weld sleeve is received in a recess adjacent the outer peripheral surface of the lead body and the prominent member is inserted into the aperture of the tubular electrode. A laser beam is directed transversely through the aperture of the electrode and onto the prominent member to simultaneously melt the prominent member and the electrode in the region of the aperture and create a mixture of the molten material of both the prominent member and the electrode within the aperture. When operation of the laser beam ceases, a welded connection between the crimp/weld sleeve and the electrode is achieved.