Various embodiments include a plate-fin type heat exchanger constructed from foil-fin layers of corrugated fins sandwiched between two sheets of thin metal plate or foil. The corrugated fins are laser welded to the metal sheets, creating continuous joints along the length of fin crests formed in the sheets by the corrugated fins. Foil-fin layers in a stack are separated by spacers or header bars to create adjacent flow paths to finned chambers with walls defined by outside faces of adjacent bonded plate-fin layers. The foil plates and the corrugated fins may be of similar or dissimilar metals. Embodiments include methods of manufacturing such heat exchangers including applying a vacuum to an assembly of corrugated fins sandwiched between sheets of thin metal plate or foil, causing fin crests in the sheets, mapping locations of the fin crests, and using the map to perform high speed laser welding along the fin crests.