An apparatus and method are disclosed that enable a private branch exchange to determine that a voice mail system has answered a call, without some of the disadvantages in the prior art. The private branch exchange--or, generally-speaking, a data-processing system--infers that the voice mail system has answered a call by timing key events or by noting some of indications that are received from another system, or both. Subsequently, the private branch exchange drops the voice mail system from the call, thereby minimizing the non-enterprise voice mail system's handling of calls that are originated to an on-premises terminal.