A high-span anchoring system is described for a cavity wall incorporating a wall reinforcement combined with a wall tie which together serve a wall construct having a larger-than-normal cavity. Further the various embodiments combine wire formatives which are compressively reduced in height by the cold-working thereof. Among the embodiments is a veneer anchoring system with a low-profile wall tie for use in a heavily insulated wall. The compressively reduced in height wall anchors protrude into the cavity through the seams, between insulation strips, which seams seal thereabout and maintain the integrity of the insulation by minimizing air leakage. Further, the eye wires extend across the insulation into the cavity between the wythes, and each accommodates the threading thereinto of a wire facing anchor or wall tie with either a pintle inserted through the eye or the open end of the veneer tie. The veneer tie is then positioned so that the insertion end is embedded in the facing wall. The close control of overall heights permits the mortar of the bed joints to flow over and about the wall reinforcement and wall tie combination inserted in the inner wythe and insertion end of the wall in the outer wythe. Because the wire formatives hereof employ extra strong material and benefit from the cold-working of the metal alloys, the high-span anchoring system meets the unusual requirements demanded thereof.