Volume-integral equations have proven to be very successful in the computation of eddy-current probe-flaw responses for NDE problems having a number of simple geometries. This approach to NDE computations has proven superior to the finite-element approach in both accuracy and computer resources required, and is the basis of our proprietary code VIC-3D1. The volume-integral approach, however, is not as well adapted to accommodating the complex geometries sometimes required in practical applications. An example is the separation of edge and corner effects from the response of a flaw. We will discuss an extension of the volume-integral approach that incorporates boundary-integral equations to provide a description of complicated surface geometries.