The increasing pervasiveness of mobile devices with networking capabilities has led to the emergence of Mobile Delay Tolerant Networks (MDTNs). The characteristics of MDTNs, which include frequent and long-term partitions, make message routing a major challenge in these networks. Most of the existing routing protocols either allocate an unlimited number of message copies or use a fixed number of message copies to route a message towards its destination. While the first approach unnecessarily oods the network, the rigidity of the second approach makes it inefficient from the viewpoint of message replication. Hence, the question that we address in this paper is: "how to dynamically allocate message copies in order to strike a balance between the delay and cost of message delivery?". We present a novel adaptive multi-step routing protocol for MDTNs. In each routing step, our protocol reasons on the remaining time-to-live of the message in order to allocate the minimum number of copies necessary to achieve a given delivery probability. Experiment results demonstrate that our protocol has a higher delivery ratio and a lower delivery cost compared to the state-of-the-art Spray-and-Wait and Bubble protocols.