The inverse compositional (IC) approach to image alignment uses characteristics of the alignment problem to improve optimization speed. While a number of authors have noted its usefulness, to date it has only been explored for least-squares type image difference measures using Gauss- Newton optimization schemes. We extend the IC approach to general difference measures, and a wider class of optimization approaches, with specific development for normalized correlation and mutual information using the BFGS optimizer. We present alignment experiments on image pairs of several different classes that demonstrate performance improvements for the general case.