The ideal-MHD analysis of tilting is extended to arbitrary plasma pressure and configuration with the limitation that the separatrix and wall remain nearly spherical. An expansion about the lowest-order eigenmode, a rigid rotation, is used to reduce δW to surface integrals involving only known equilibrium quantities. Previous results are recovered, showing that elliptically prolate structures are unstable for a wall outside the separatrix and elliptically oblate structures are stable with a conducting shell close but outside the separatrix. New results include: non-elliptical prolate shapes can be stable (problimaks); a wall inside the separatrix is stabilizing; stability is insensitive to the magnitude of the plasma pressure but somewhat sensitive to the current profile; at fixed wall-surface area, factors of two in the stability conditions are achieved by changing the separatrix and wall shapes.