This paper presents a new real-time Quality of Service (QoS) scheme, called Relaxed (m, k)-firm, for multimedia flow transmission which can tolerate occasional packet drops. In contrast to traditional real-time constraint, Relaxed (m, k)-firm requires the transmission delay constraint on a group of any k consecutive packets instead of imposing a transmission delay constraint per packet. Due to this relaxation, this novel scheme can achieve high resource utilisation. A new traffic control mechanism, called Double-Leaks Bucket (DLB), is also proposed to selectively drop a proportion of packets in case of network congestion while still guaranteeing the R-(m, k)-firm constraint.