Motivated by an application in thin wire visualization, we study an abstract on-line scheduling problem. Unlike most scheduling problems, our schedulers can gain partial merit from a partially served request. Thus our problem embodies a notion of “Level of Service” that is increasingly important in multimedia applications. We give two schedulers FirstFit and EndFit based on two simple heuristics, and generalize them into a class of greedy schedulers. We show that both FirstFit and EndFit are 2-competitive, and any greedy scheduler is 3-competitive. These bounds are shown to be tight.