Track-oriented multiple-hypothesis tracking is a powerful and widely-accepted methodology in multi-target tracking. We show that the target-death problem inherent in the probability hypothesis density filter does not arise in the MHT. However, the MHT suffers from a problem of its own: excessive competition for measurements from tentative tracks. We introduce a mechanism to mitigate this effect by favoring confirmed tracks in the association process. A heuristic justification for the technique is that it mitigates the sub-optimality associated with hypothesis pruning and sequential track extraction. Perhaps more convincingly, the modification to the MHT equations is provably optimal in the limiting case of cardinality tracking with unity detection probability. We show that modified-scoring MHT improves upon standard MHT in several benchmark studies.