This paper summarizes the general theory of the Gregorig fluted condensing surface, and includes advances since Gregorig’s original publication. These include Bromley, et al.’s mathematical description for the geometrical shape of the convex surface, and definition of the “optimum” fluted surface geometry established by Zener and Lavi. However, their optimization is applicable to only one of a family of possible convex surface shapes. This paper extends the work of Zener and Lavi to define the optimum geometry as a function of the included angle of the convex surface. This broader optimization analysis will support calculation of economically optimum fluted surface designs. Calculated results are presented for ammonia condensing on vertical fluted tubes and compared with existing experimental data. The expected performance of real condensers is discussed, relative to the idealized conditions assumed in the analysis. Finally, the paper outlines a step-by-step procedure for the design of the fluted surface and construction of the convex surface profile.