A typical modern telescope control system points by first calculating the direction of the target in nominal mount coordinates and then applying small corrections to the demanded mount angles. The pointing refers to the rotation axis of the instrument mount, and rotator demands are calculated via parallactic angle. This simple approach works well enough when the corrections are small and the accuracy objectives are modest. However, a more rigorous approach can pay off, in the form of improved pointing, more accurate guide probe predictions, reduced residual field rotation and reliable world coordinate system information even when the detector is off-axis. In this paper I propose a rigorous vector/matrix algorithm for generating pointing predictions on an imperfect telescope, with support for autoguiding, field stabilization and world coordinate systems even in difficult cases such as Nasmyth and coude.