Skeletal subspace deformation (SSD), a simple method of character animation used in many applications, has several shortcomings; the best-known being that joints tend to collapse when bent. We present animation space, a generalization of SSD that greatly reduces these effects and effectively eliminates them for joints that do not have an unusually large range of motion.While other, more expensive generalizations exist, ours is unique in expressing the animation process as a simple linear transformation of the input coordinates. We show that linearity can be used to derive a measure of average distance (across the space of poses), and apply this to improving parametrizations.Linearity also makes it possible to fit a model to a set of examples using least-squares methods. The extra generality in animation space allows for a good fit to realistic data, and overfitting can be controlled to allow fitted models to generalize to new poses. Despite the extra vertex attributes, it is possible to render these animation-space models in hardware with no loss of performance relative to SSD.