ATM-based integrated services networks are likely to rely on the Virtaal Path (VP) concept as an intermediate resource management layer wherein key decisions concerning resource allocation, sharing, and flow aggregation are made. In this paper we consider the impact that statistically multiplexing heterogeneous services on VP connections will have on network design and management. Based on simple models we consider several questions with perhaps surprising answers including the following. Given two traffic types with different quality of service requirements, should one segregate such flows on their own VPS, or is it to the network's advantage to multiplex the flows on a single VP guaranteeing the most stringent QoS requirement? Assuming two VPs have been set up between a given origin-destination pair and heterogeneous flows are to be carried, how should one route the connections to achieve good performance?