One illustrative method disclosed herein includes, among other things, forming first and second fins, forming a liner layer above at least a first upper surface of the first fin and a second upper surface of the second fin, and forming an ion-containing region in the first portion of the liner layer while not forming the ion-containing region in second portion of the liner layer. The method also includes performing a liner etching process so as to remove the second portion of the liner layer while leaving at least a portion of the first portion of the liner layer positioned above the first fin, and performing at least one etching process to define a reduced-height second fin that is less than an initial first height of the first fin.