One illustrative method disclosed herein includes forming a patterned hard mask layer comprised of a plurality of discrete openings above a structure, wherein the patterned hard mask layer is comprised of a plurality of intersecting line-type features, forming a patterned etch mask above the patterned hard mask layer that exposes at least one, but not all, of the plurality of discrete openings, and performing at least one etching process through the patterned etch mask and the at least one exposed opening in the patterned hard mask layer to define an opening in the structure.