Statistical gain is achieved in asynchronous transfer mode (ATM) networks by making bursty connections share resources stochastically. When connections with different QOS requirements share the same resources, the highest QOS requirements would typically be the limiting factor in determining the admissible load at a link. This may lead to connections with low QOS requirements getting better service than they require, leading to an underutilization of the resources. To alleviate this problem, a burst-level priority scheme is proposed. In the proposal, burst of related cells are to be handled in the network on a burst-by-burst basis. Bandwidth is allocated to bursts on-the-fly according to their priorities. This proposal includes a two-level priority CAC scheme for controlling the burst-level blocking rates of independent heterogeneous on-off sources.