A method of applying a veneer exterior wall system, the method having the steps of attaching a weep screed substantially horizontally on a wall at a location where a veneer has a termination edge; attaching a weather barrier layer over an outward side of the wall, the weather barrier extending downward and terminating at the upper flange; attaching a drainage mat over on an outward side of the weather barrier, the drainage mat extending downward and terminating at the upper flange, wherein the apertures are directly below at least a portion of the drainage mat; attaching a mesh over on an outward side of the drainage mat, the mesh extending downward and terminating at the upper flange; and applying at least one coat of plaster over the mesh, the coat of plaster extending downward and terminating at the upper flange.