One illustrative method disclosed herein involves forming gate structures for first and second spaced-apart transistors above a semiconducting substrate, forming an etch stop layer above the substrate and the gate structures, performing at least one angled ion implant process to implant at least one etch-inhibiting species into less than an entirety of the etch stop layer, after performing at least one angled ion implant process, forming a layer of insulating material above the etch stop layer, performing at least one first etching process to define an opening in the layer of insulating material and thereby expose a portion of the etch stop layer, performing at least one etching process on the exposed portion of the etch stop layer to define a contact opening therethrough that exposes a doped region formed in the substrate, and forming a conductive contact in the opening that is conductively coupled to the doped region.