Existing archives of asteroid observations contain many objects with very short observed arcs. In this paper we present a method that we have used with considerable success to attribute these short arc \discoveries" to other objects with better dened orbits. The method consists of a three stage ltering process whereby several billion possible attribution/orbit pairs are systematically analyzed with more and more exact algorithms, at each stage rejecting improbable cases. The rst stage compares an attributable, by denition a synthetic observation representative of all the observations over a short arc, with the predicted observation for each available orbit. The second stage compares the proposed attributable observations with predicted positions from the known orbit using conventional linear covariance techniques, considering both the position and motion on the celestial sphere. In the nal lter we attempt to compute a best tting orbit by dierential corrections and using the com..