One illustrative method disclosed herein includes, among other things, forming an original fin-formation etch mask comprised of a plurality of original line-type features and removing at least a portion of at least one of the plurality of original line-type features so as to thereby define a modified fin-formation etch mask comprising the remaining portions of the plurality of original line-type features. The method also includes forming a conformal layer of material on the remaining portions of the plurality of original line-type features of the modified fin-formation etch mask and performing at least one etching process to remove at least portions of the conformal layer of material and to define a plurality of fin-formation trenches so as to thereby initially define a plurality of fins in the substrate.