Methods for enabling call center agents to adapt their servicing of incoming calls based on the estimated value of the calls are disclosed. In accordance with the first illustrative embodiment, when there is a “high-value” call waiting in the queue while one or more agents are currently servicing lower-value calls, an agent who is servicing a lower-value call is informed that there is a higher-value call waiting in the queue, and is prompted to provide an estimate of how much longer he or she will be servicing his or her current call. The call center system selects which agent the high-value call will be routed to based on: (i) the agents' responses to the prompts, and (ii) for each of the responding agents, a measure of how closely prior responses from the agent compared to the actual amount of time taken by the agent to complete servicing the call.