Welded high-density low-profile interconnect system

An electronic device may have printed circuits to which electrical components are mounted. The printed circuits may have metal traces that form signal lines and contact pads. Vias or other conductive structures may be used in interconnecting the signal lines to the contact pads. The contact pads may have elongated shapes or other shapes and may be formed in arrays on the printed circuits. Laser welds or other electrical connections may be used to join contact pads on a first printed circuit to respective contact pads on a second printed circuit. The laser welds may form part of a rectangular region of welds or may form part of a non-rectangular region of welds such as a region with a curved edge. Alignment marks may be used in aligning the contact pads.