A method for reconstructing the complex index of refraction of a bounded inhomogeneous object from measured scattered field data is presented. The index and the unknown fields within the object are simultaneously reconstructed in an iterative algorithm. The method is a refinement of earlier work which incorporates a more effective way to update the unknowns at each stage of the iteration. Considerable efficiency in the algorithm is achieved. Some numerical examples are given indicating the limits on the contrasts which can be reconstructed. These limits show that the range of contrasts that may be reconstructed is extended over that achievable with the earlier work.