A method, apparatus, and customer contact or call server that provides a unified queuing mechanism for queuing multiple media requests. The queuing mechanism includes one or more skillsets each including an idle agent queue and a pending requests queue. Skillsets are assigned interrupt levels defining the importance of skillsets with respect to each other. Agents are assigned to and queued in the idle agent queue of one or more of the skillsets. As media requests are received in the pending requests queues of skillsets, agents are dispatched to attend to the requests. As an agent is dispatched from a skillset, it is removed from other skillsets that have an equal or lower interrupt level, and is maintained in skillsets that have a higher interrupt level. Consequently, an agent, tending to a media request, may be interrupted with other media requests only if the other media requests are queued in skillsets of higher interruptibility level, and if the agent is assigned to those other skillsets. Media requests include, among other things, a voice/video call request, an e-mail request, a web form request, and an outbound voice call request.