The complete Bouguer reduction includes, in addition to the simple Bouguer slab correction (Bullard A), both curvature (Bullard B) and terrain (Bullard C) corrections. A new closed-form formula for the curvature correction is derived for which the calculated values differ from those published by Swick by more than 0.5 mGal for high elevations. These corrections reduce those of an infinite slab (Bullard A) to that of a spherical cap having a surface radius of 166.7 km. The spherical cap produces a lesser effect than the infinite slab because of the 'truncation' of that part of the slab above the earth and extending to infinity, but it produces a greater effect than the slab because of subslab earth resulting from curvature. The physical significance of the correction lies in the combination of these two differences, which are each a function of elevation. The Bullard B surface radius (166.7 km: outer radius of the Hayford-Bowie system) is reaffirmed by the exact formula to be appropriate for exploration surveys. Three series approximations are presented and compared, but the exact Bullard B formula is very efficient and easy to program for routine data processing.