One illustrative method disclosed herein includes, among other things, forming an opening in a layer of insulating material so as to thereby expose at least a portion of a conductive contact, performing a selective deposition process to selectively form a layer of conductive material in the opening and on the conductive contact, performing an anneal process, depositing at least one conductive material above the selectively formed conductive material layer so as to over-fill the opening, and performing at least one planarization process so as to remove excess materials to thereby define a conductive via that is positioned in the opening and conductively coupled to the conductive contact.