Active Appearance Models (or AAMs) are fast linear models for appearance variation in images. A key disadvantage of AAMs is the requirement for hand-labeled correspondence points. We use Morphable Model (or MM) data to avoid hand-labeling error and test the convergence performance of a well known fitting method, Inverse Compositional Image Alignment (or ICIA). The 3D MM data is in dense correspondence forms the ground truth for AAM fitting. Using ICIA, we investigate the robustness of AAM convergence with respect to rigid-body transformations and lighting of these 3D models. It is found that a contour fitting problem arises in AAMs and dominates the standard RMS error computation; an alternative measure is presented. A different composition method using QR factorization is presented, and also preliminary results of fitting AAMs built using MM training data to real images is presented.