Disclosed herein are various methods of forming conductive contacts with reduced dimensions and various semiconductor devices incorporating such conductive contacts. In one example, one method disclosed herein includes forming a layer of insulating material above a semiconducting substrate, wherein the layer of material has a first thickness, forming a plurality of contact openings in the layer of material having the first thickness and forming an organic material in at least a portion of each of the contact openings. This illustrative method further includes the steps of, after forming the organic material, performing an etching process to reduce the first thickness of the layer of insulating material to a second thickness that is less than the first thickness, after performing the etching process, removing the organic material from the contact openings and forming a conductive contact in each of the contact openings.