Algorithms for self-calibrating cameras whose changes in calibration parameters are confined to rotation and zooming are useful since many real-world imaging situations do not permit translations-consider, for instance, cameras mounted on tripods and desk or wall-mounted active heads. In practice, however, the assumption of pure rotation is often violated because the optic center of the camera and the rotation center do not completely coincide. This work determines how such misalignments affect the estimation of the camera focal length. Expressions for the errors in focal length and recovered rotations are derived and results are confirmed with experiments on synthetic data. We show that the approximation of pure rotation is indeed sufficient in many cases, especially since other sources of error, such as noise and particularly radial distortion, tend to be more detrimental.