The Differentiated Services (DiffServ) approach is intended to provide Quality of Service (QoS) in IP-based networks. This is a very important issue not only in wire-line fixed networks but also in IP-based wireless mobile networks. Currently, services within the DiffServ approach including Premium Service, Assured Service and Best-Effort Service are intended for fixed networks. We have proposed the Mobile Differentiated Services QoS model [5] to enhance the above services so they are better suited for wireless mobile networks. One part of this QoS model is the socalled Best-Effort Low-Delay (BELD) Service which has the same low-delay and low-jitter characteristic as Premium Service, but a certain probability for packet loss. This service is especially suited for delay-sensitive and loss-tolerant applications and can take favor of unused Premium Service resources to increase the network utilization. This paper presents details on the BELD Service including initial simulation results...