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This paper describes the development of high-order Kirchhoff algorithms and confirms that high-order accuracy can be achieved with the Kirchhoff approach when high-order integration and interpolation are properly implemented. This paper also establishes guidelines for enhancing accuracy of a given order property when the Kirchhoff formula is applied to results obtained from a computational fluid dynamics (CFD) solution. Accuracy is shown to increase when the Kirchhoff surface size is minimized. Reduction of the Kirchhoff surface size also enhances efficiency of the calculation because the size of the relatively expensive CFD computation is reduced. The accuracy of the Kirchhoff approach is also enhanced by increasing the density of information along the Kirchhoff surface. This increase in information is necessary because evaluation of the Kirchhoff integrand at the retarded time demands higher spatial resolution than the integration of the time-dependent nonlinear equations of the CFD calculation. A procedure has been developed that addresses the Kirchhoff resolution requirements without sacrificing efficiency. The error reduction realized with this procedure matches that realized with CFD mesh refinement, with almost no increase in cost.