As computational Grids become an increasingly dominant force in the high-performance computing arena, the problem of efficiently transferring very large data sets, across geographically distributed computing resources, becomes increasingly difficult and important. Current approaches view the problem largely, if not exclusively, as a network-level problem. Thus all packet loss is interpreted and treated as a network congestion event, limiting the ability to detect or react to changes in the end-to-end system. We believe that a new approach to this problem is worth pursuing, and we are investigating techniques that can differentiate between data loss caused by contention in the network and loss caused by contention for shared CPU resources at the communication endpoints. The approach is to collect and analyze what we term packet-loss signatures that describe the patterns of packet-loss in the current transmission window. We analyze these signatures using Fourier analysis and symbolic dynamics, and present a simple set of experiments demonstrating the effectiveness of this approach. Our longer-term goal is to exploit such information in next-generation congestion control mechanisms.