Recent advances in deconvolution have allowed positive images to be deconvolved without prior knowledge of either of the images comprising the convolution. We incorporate these methods into the shift-and-add principle by exploiting the property of the basic shift-and-add image that it is a (noisy) convolution of the true image of an object with some unknown point-spread-function. This allows an estimate of the true image to be extracted from the shift-and-add image. The computational efficiency of basic shift-and-add is preserved during data gathering since extensive computation is only applied to a single image. Results are presented of a computer simulation of the technique, indicating that it can remove the "ghosts" which are present in the basic shift-and-add image of a multiple star.