This paper presents a new set of forwarding behaviors that fits rate-adaptive and delay-sensitive applications with limited loss tolerance. We consider an application to have limited loss tolerance if it needs loss-free forwarding of specific packets up to a certain rate. The new set of forwarding behaviors are attractive for developing real-time applications for the Internet. In particular, such applications can be designed to use reserved forwarding capacity efficiently and compete for more bandwidth while being fair to best-effort traffic. To provide the new set of forwarding behaviors, we define a scheduling mechanism that can be implemented efficiently. Through simulations, we show that this mechanism supports the defined forwarding behaviors.