The problem of efficiently delivering data within networks is very important nowadays, especially in the context of the large volumes of data which are being produced each year and of the increased data access needs of the users. Efficient data delivery strategies must satisfy several types of Quality of Service (QoS) constraints which are imposed by the data consumers. One possibility of achieving this goal (particularly in the case of in-order data transfers) is to choose a satisfactory network delivery path. In this paper we present novel algorithmic approaches for computing optimal network paths which satisfy several types of (QoS) constraints.