Rate-Delay (RD) Network Services constitute a promising differentiated-services architecture for multi-provider networks, by offering users a choice between high throughput or low queuing delay at bottleneck links. An RD router provides service differentiation via transmission scheduling and by managing two FIFO queues. To ensure strict delay bounds, an RD router tracks arrival times of packets in the D service queue, and discards late packets at the queue head. However, maintaining the per-packet state is undesirable for complexity and cost reasons. In this paper, we present a Stateless RD (S-RD) router design that provides low queuing delay to the D service exclusively via buffer dimensioning, without requiring any per-packet state. After proving analytically that the S-RD design meets the delay guarantees, we use simulation to evaluate the performance of the stateless design, confirming that S-RD routers preserve the delay bounds of RD network services. As case studies, we consider Voice-over-IP (VoIP) and Web browsing as particular examples of Internet applications. The extensive simulation results demonstrate that S-RD Network Services significantly improve VoIP quality and increase the goodput of short-lived Web flows, without degrading the throughput of long-lived flows.