A method is disclosed that enables the proper treatment of a queued call by a call center, or other data-processing system capable of queuing calls, in which the calling terminal of the queued call has been put on hold by its user. The call center is able to detect the terminal being put on hold by monitoring for a SIP re-INVITE request, in which the session description signifies an on-hold condition. When it is determined that the calling terminal is on hold, the call center modifies its treatment of the queued call. For example, the call center might freeze the call's position in the queue until the calling party takes the phone off of hold. As another example, the call center might allow the call to work its way to the top of the queue, with the terminal on hold, and then maintain the call's position at the top of the queue until a service agent is available.