In multi-unit auctions, such as auctions of commodities and securities, and financial exchanges, it is necessary to specify rationing rules to break ties between multiple marginal bids. The standard approach in the literature and in pratice is to ration marginal bids proportionally. This paper shows how bidding can be made more competitive if the rationing rule instead gives increasing priority to bidders with a small volume of marginal bids at clearing prices closer to the reservation price. In comparison to standard rationing, such a rule can have almost the same effect on the competitiveness of bids as a doubling of the number of bidders.