The Asynchronous Transfer Mode (ATM) has been developed as a connection-oriented technique for the transfer of fixed-size cells over high-speed networks. Many applications, however, require a connectionless network service. In order to provide such a technique, one can build a connectionless service on top of the connection-oriented service. In doing so, the issue of connection management comes into play. We propose a new connection management mechanism that provides for low bandwidth usage (as compared to a permanent connection) and low delays (as compared to a connection-per-packet approach). We model the new mechanism under two workload scenarios: an ordinary Poisson process and an interrupted Poisson process. We use Markovian techniques as well as matrix-geometric methods to evaluate the new connection management mechanism. From the evaluations it turns out that the proposed mechanism is superior to older approaches (which can be seen as limiting cases).