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We present Asymmetric Best-Effort (ABE), a novel service to provide a throughput versus delay jitter service for IP packets. With this service, every best effort packet is marked as either Green or Blue. Green packets, typically sent by real-time applications such as interactive audio, receive more losses during bouts of congestion than Blue ones. In return, they receive a smaller bounded queueing delay. Both Green and Blue services are best-effort. The incentive to choose one or other is based on the nature of one`s traffic and on traffic conditions. If applications are TCP-friendly, an application sending Blue packets will receive more throughput but also more delay jitter, than it would if it sent Green packets for a given network state and path. Service provision at each co-operating router can be achieved by Packet Admission Control (PAC)and scheduling. We develop and simulate an initial lgorithm that supports this service whose first results show the feasibility of the service.