In this report, we consider communication networks with a satellite with multiple spot beams. We describe the structure and features of these networks, and we consider admission control schemes which optimize the network revenue if several services types with different revenues are present. We show that in some cases the blocking of some calls even if capacity is available can considerably increase the network revenue. We will point out, however, that complete sharing, i.e., accepting calls on a first- come, first-served basis, is optimum for systems with similar traffic types.