A multi-step electrochemical method for forming a copper metallurgy on an integrated circuit which has high aspect ratio contact/via openings is described. The method is designed to give good coverage and gap filling capability as well as high production throughput by depositing the copper in two stages with an optional dwell period between the stages. The process utilizes a copper plating electrolyte which contains an added brighteners and levelers. A first copper layer is plated at a low current density which provides good coverage resulting from a high throwing power. The high aspect ratio openings are covered with a substantial thickness of a uniform, high quality copper coating. During plating, the concentration of brightener becomes depleted in the base region of high aspect ratio contacts or vias. Optionally, the brightener is replenished in these regions during a brief dwell period wherein the plating current is stopped. Next, a high current density is applied whereby the openings are filled and additional copper is deposited over them at a high deposition rate. A benefit of the high current density deposition is that depletion of leveler chemical in the openings enhances the growth rate of copper at the base of the openings thereby favoring growth from bottom up. This avoids the formation of voids in the openings. The greatest throughput benefits are realized, by way of the high current density step, when the process is applied to the formation of a dual damascene metallurgy.