One illustrative transistor of a first dopant type disclosed herein includes a gate structure positioned above a semiconductor substrate and first and second overall epitaxial cavities formed in the semiconductor substrate on opposite sides of the gate structure. The device also includes a counter-doped epitaxial semiconductor material positioned proximate a bottom of each of the first and second overall epitaxial cavities, wherein the counter-doped epitaxial semiconductor material is doped with a second dopant type that is opposite to the first dopant type, and a same-doped epitaxial semiconductor material positioned in each of the first and second overall epitaxial cavities above the counter-doped epitaxial semiconductor material, wherein the same-doped epitaxial semiconductor material is doped with a dopant of the first dopant type.