Object pose estimation is a difficult task due to the non-linearities of the projection process; specifically with regard to the effect of depth. To overcome this complication, most algorithms use an error metric which removes the effect of depth. Recently, two new algorithms have been proposed based upon iteratively improving pose estimates obtained with weak-perspective or paraperspective approximations of the projection equations. A simple technique for improving the estimates of the two projection approximation algorithms is presented and a new metric is proposed for use in 'polishing' these object pose estimates. At all distances, the new algorithm reduces the estimated orientation error by over ten percent. At short distances, the orientation improvement is about seventeen percent and the position error is reduced by twelve percent.