The optimal cross-sectional shapes of clampedsimply supported columns are presented with the compressive load given by a combination of a non-uniform distributed load and a concentrated load. The buckling load is maximized subject to constraints on the volume of the column and on the maximum stress. The non-symmetry of the boundary conditions leads to optimal shapes which depend on the direction of the distributed load, with the optimal cross-section getting larger in the direction of the distributed load. This is a major difference in the optimal design of columns with symmetrical and asymmetrical boundary conditions when subjected to distributed axial loads. The minimum cross-sectional area is not known a priori in the case of a stress constraint since this depends on the buckling load, which in turn depends on the optimum shape. This aspect is the main difference between the optimal designs of area-constrained and stress-constrained columns. An iterative method is developed to compute the optimal shapes with the analysis performed using a finite element method. Results are given for various combinations of distributed and concentrated loads and constraints. Results for optimal columns with a minimum area constraint are also given for comparison purposes.