In this paper, we investigate an economically motivated session-aware admission-control model for Internet servers subjected to future NGN session-oriented services. Our fundamental observation is that it is sometimes desirable to reject new sessions from some customers, so that others may be completed and thereby generate some revenue for the operator. Conversely, most of the already existing admission-control schemes, which operate either at the packet level or at the request level, may interrupt life-service sessions at any time during their lifespan. In this work, we evaluate novel service-oriented sessionaware admission-control strategies for controlling the acceptance of the offered network traffic to an Internet server. Conducted simulations target popular VoIP service. Simulation results demonstrate that responsive session-aware admission control improves the service provider's benefit and offers better QoS to subscribers. Particularly, we show that session-aware responsiveness provides network QoS in terms of completion of the service sessions independently of their durations.