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Deregulated electricity markets use an auction mechanism to select offers and their power levels for energy and ancillary services. A settlement mechanism is then used to determine the payments resulting from the selected offers. Currently, most independent system operators (ISOs) in the United States use an auction mechanism that minimizes the total offer costs but determine payment costs using a settlement mechanism that pays uniform market clearing prices (MCPs) to all selected offers. Under this setup, the auction and settlement mechanisms are inconsistent since minimized costs are different from payment costs. Illustrative examples in the literature have shown that for a given set of offers, if an auction mechanism that directly minimizes the payment costs is used, then payment costs can be significantly reduced as compared to minimizing offer costs. This observation has led to discussions among stakeholders and policymakers in the electricity markets as to which of the two auction mechanisms is more appropriate for ISOs to use. While methods for minimizing offer costs abound, limited approaches for minimization of payment costs have been reported. This paper presents an effective method for directly minimizing payment costs. In view of the specific features of the problem including the nonseparability of its objective function, the discontinuity of offer curves, and the maximum term in defining MCPs, our key idea is to use augmented Lagrangian relaxation and to form and solve offer and MCP subproblems by using the surrogate optimization framework. Numerical testing results demonstrate that the method is effective, and the resulting payment costs are significantly lower than what are obtained by minimizing the offer costs for a given set of offers.