Abstract.  This paper is concerned with the on-line problem of scheduling jobs with tight deadlines in a single-processor system. It has been known for long that in such a setting, no on-line algorithm is optimal (or 1-competitive) in the sense of matching the optimal off-line algorithm on the total value of jobs that meet the deadlines; indeed, no algorithm can be Ω(k)-competitive, where k is the importance ratio of the jobs. Recent work, however, reveals that the competitive ratio can be improved to O(1) if the on-line scheduler is equipped with a processor O(1) times faster; furthermore, optimality can be achieved when using a processor O(log k) times faster. This paper presents a new on-line algorithm for scheduling jobs with tight deadlines, which can achieve optimality when using a processor that is only O(1) times faster.