The task of registering two coordinate frames is frequently accomplished by measuring the same set of points in both frames. Noise and possible bias in the measured locations degrade the quality of registration. It was shown that the performance of registration may be improved by filtering out noise from repeated measurements of the points, calculating small corrections to the mean locations and restoring rigid-body condition. In the current study, we investigate experimental conditions in which improvement in registration can still be achieved without cumbersome collection of repeated measurements. We show that for sufficiently small noise relative to bias, the corrections calculated from a single measurement of points can be used and still lead to the improved registration.