Messages in delay-tolerant networks (DTNs) are generally classified by relative priority into low, medium, and high priority classes, thus creating challenges in structuring scheduling and drop policies of a traffic management system. This study proposes a novel traffic management strategy for DTNs. The proposed scheme improves message deliveries of different priority classes by utilizing message properties such as estimated total number of replicas, elapsed time, and remaining time-to-live. A delete mechanism of delivered messages is also incorporated to use buffer space efficiently. The performance of the proposed strategy is verified via implementation of a simulation model along with existing scheduling and drop policies and is tested with two well-known real-world trace datasets. The results demonstrate that the proposed strategy yields improved message deliveries of high priority as well as medium and low priority classes.