The number of media streams that can be supported concurrently is highly constrained by the stringent requirements of real-time playback and high transfer rates. To address this problem, media delivery techniques, such as Batching and Stream Merging, utilize the multicast facility to increase resource sharing. The achieved resource sharing depends greatly on how the waiting requests are scheduled for service. Scheduling has been studied extensively when Batching is applied, but up to our knowledge, it has not been investigated in the context of stream merging techniques, which achieve much better resource sharing. In this study, we analyze scheduling when stream merging is employed and propose a simple, yet highly effective scheduling policy, called Minimum Cost First (MCF). MCF exploits the wide variation in stream lengths by favoring the requests that require the least cost. We present two alternative implementations of MCF: MCF-T and MCF-P. We compare various scheduling policies through extensive simulation and show that MCF achieves significant performance benefits in terms of both the number of requests that can be serviced concurrently and the average waiting time for service.