Efficient and accurate fitting of active appearance models (AAM) is a key requirement for many applications. The most efficient fitting algorithm today is inverse compositional image alignment (ICIA). While ICIA is extremely fast, it is also known to have a small convergence radius. Convergence is especially bad when training and testing images differ strongly, as in multi-person AAMs. We describe ldquoforwardrdquo compositional image alignment in a consistent framework which also incorporates methods previously termed ldquoinverserdquo compositional, and use it to develop two novel fitting methods. The first method, compositional gradient descent (CoDe), is approximately four times slower than ICIA, while having a convergence radius which is even larger than that achievable by direct quasi-Newton descent. An intermediate convergence range with the same speed as ICIA is achieved by LinCoDe, the second new method. The success rate of the novel methods is 10 to 20 times higher than that of the original ICIA method.