This paper considers the support of hard real-time connections in ATM networks. In an ATM network, a set of hard real-time connections can be admitted only if the worst case end-to-end delays of cells belonging to individual connections are less than their deadlines. Although there are several approaches to manage the network resources in order to meet the delay requirements of connections, we focus on the use of traffic regulation to achieve this objective. Leaky buckets provide simple and user-programmable means of traffic regulation. We design and analyse an efficient optimal algorithm for selecting the burst parameters of leaky buckets to meet connections' deadlines. Our algorithm is optimal in the sense that it always selects burst parameters to meet the delay requirements of hard real-time connections whenever some such assignment exists. The exponential size of the search space makes this problem a challenging one. Our algorithm is efficient and we observe a dramatic improvement in the system performance in terms of the connection admission probability when traffic is regulated using our algorithm