Differentiated Services (DiffServ) is a proposed architecture for the Internet in which various applications are supported using a simple classification scheme. Packets entering the DiffServ domain are marked depending on the packets' class. Premium service and Assured service are the first two types of services proposed within the DiffServ architecture other than the best effort service. Premium service provides a strict guarantee on users' peak rates, hence delivering the highest Quality of Service (QoS). However, it expected to charge at high rates and also to have low bandwidth utilization. The Assured service provides high priority packets with preferential treatment over low priority packets but without any quantitative QoS guarantees. In this paper, we propose a new service, which we call the Loss bound Guaranteed (LG) service for DiffServ architectures. This service can provide a quantitative QoS guarantee in terms of loss rate. A measurement-based admission control scheme and a signaling protocol are designed to implement the LG service. An extensive simulation model has been developed to study the performance and viability of the LG service model. We have tested a variety of traffic conditions and measurement parameter settings in our simulation. The results show that the LG service can achieve a high level of utilization while still reliably keeping the traffic within the maximum loss rate requirement. Indeed, we show that the DiffServ architecture can provide packet-loss guarantees without the need for explicit resource reservation.