An approximate scattering theory that utilizes the exact solutions for spherical defects is being developed. A defect of arbitrary shape can be represented by a sphere S and a remainder volume δv. By treating δv as a perturbation, one obtains an approximate solution that contains non-trivial frequency dependence and phase information. The approach is expected to be useful for studying defects with small but significant deviations (such as sharp edges) from spherical shape.