One illustrative method disclosed herein includes, among other things, removing at least one, but not all, of a plurality of first features in a first patterned mask layer so as to define a modified first patterned masking layer, wherein removed first feature(s) correspond to a location where a final isolation structure will be formed, performing an etching process though the modified first patterned masking layer to form an initial isolation trench in the substrate, and performing another etching process through the modified first patterned mask layer to thereby define a plurality of fin-formation trenches in the substrate and to extend a depth of the initial isolation trench so as to define a final isolation trench for the final isolation structure.