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Overlay multicast is an effective approach to the problem of streaming distribution. Other approaches proposed for streaming, i.e., unicast transmission and IP multicast have several drawbacks. The former method is not scalable with the growing number of users. The latter method - IP multicast - requires strong cooperation with ISPs (Internet Service Providers) what is not always realizable due to business issues. Based on our previous works, we focus on solving the overlay network design problem to economically distribute content among the participants using overlay multicast. The optimization goal is to minimize the overlay network cost expressed by the cost of access links. Additionally, we assume that the maximum total delay of a streaming tree is upper bounded to provide QoS (Quality of Service) guarantees. We show how various constraints following from real overlay systems influence the behavior of the distributing system. In numerical experiments we use real ISPs' price lists. To illustrate our approach we present optimal results obtained from the CPLEX solver.