Copper plating baths containing a leveling agent that is a reaction product of a compound including a heteroatom chosen from nitrogen, sulfur and a mixture of nitrogen and sulfur, with a polyepoxide compound containing an ether linkage that deposit copper on the surface of an electronic device and in apertures on such substrate are provided. Such plating baths deposit a copper layer on the substrate surface that is substantially planar across a range of electrolyte concentrations. Methods of depositing copper layers using such copper plating baths are also disclosed.