End-to-end QoS requires mapping of performance metrics between sub-networks of the end-to-end system. In this work, we map loss and delay between IP Integrated Services (intserv) and ATM, using deterministic service curves. First, we recall our method for mapping of backlog, loss and delay between a single IP flow and ATM. Second, we extend our mapping method to the case of the three intserv classes served by an ATM switch implementing a priority-based discriminatory discipline. Third, we focus on cases of non-conformant traffic and congested systems. Extensive numerical simulations yield qualitative as well as quantitative mapping of loss and delay between intserv and ATM.