3D morphable models, as a means to generate images of a class of objects and to analyze them, have become increasingly popular. The problematic part of this framework is the registration of the model to an image, a.k.a. the fitting. The characteristic features of a fitting algorithm are its efficiency, robustness, accuracy and automation. Many accurate algorithms based on gradient descent techniques exist which are unfortunately short on the other features. Recently, an efficient algorithm called inverse compositional image alignment (ICIA) algorithm, able to fit 2D images, was introduced. We extent this algorithm to fit 3D morphable models using a novel mathematical notation which facilitates the formulation of the fitting problem. This formulation enables us to avoid a simplification so far used in the ICIA, being as efficient and leading to improved fitting precision. Additionally, the algorithm is robust without sacrificing its efficiency and accuracy, thereby conforming to three of the four characteristics of a good fitting algorithm.