Embodiments of a method for fabricating integrated circuits are provided, as are embodiments of an integrated circuit. In one embodiment, the method includes the steps of depositing an interlayer dielectric (“ILD”) layer over a semiconductor device, depositing a barrier polish stop layer over the ILD layer, and patterning at least the barrier polish stop layer and the ILD layer to create a plurality of etch features therein. Copper is plated over the barrier polish stop layer and into the plurality of etch features to produce a copper overburden overlying the barrier polish stop layer and a plurality of conductive interconnect features in the ILD layer and barrier polish stop layer. The integrated circuit is polished to remove the copper overburden and expose the barrier polish stop layer.