A detailed asymptotic analysis accounting for wall curvature extends the Brenner-Gaydos formula for the hydrodynamic hindrance factor (J. Colloid Interface Sci. 1977, 58, 312-356) to terms of order lambda(2), yielding a new result of the form (D) over bar/D infinity = (1 - lambda)(-2) [1 + (9/8)lambda ln lambda - 1.539 lambda + C-2 lambda(2) + o(lambda(2))], with C-2 approximate to 1.2, where lambda denotes the ratio of solute to pore radii. The accuracy of approximate formulas for (D) over bar is assessed definitively by comparison with recent boundary element calculations and experiments.