One illustrative method disclosed herein includes, among other things, forming a plurality of fins in a semiconducting substrate, each of which has a corresponding masking layer feature positioned thereabove, forming a masking layer that has an opening that exposes at least two fins of the plurality of fins, performing an angled etching process through the opening in the masking layer so as to remove the masking layer feature formed above one of the at least two exposed fins, and thereby define an exposed fin, while leaving the masking layer feature intact above the other of the at least two exposed fins, and performing an anisotropic etching process through the opening in the masking layer to remove the exposed fin while leaving the other of the at least two exposed fins intact.