A method for alleviating congestion problems in prior art networks delays provision of dial tone signals to terminals that are, likely, carrying out a re-dial attempt in excess of a preselected number of re-dial attempts. A determination that the terminal seeking to establish a connection is likely carrying out a re-dial attempt may be based on numerous factors, such as the time since the last time the terminal desired to establish a call, the duration of the last call, etc. The delay that is imposed is, advantageously, sensitive to the number of times the terminal has attempted a re-dial, and on other conditions, such as the cause of the failure to establish a connection, network congestion conditions, etc. In imposing the dial tone delay, identities of the terminals that are to receive a delayed dial tone are placed in a FIFO queue.