Current work in the IETF aims at providing service differentiation on the Internet. One proposal is to provide loss differentiation by assigning levels of drop procedence to IP packets. In this paper, we evaluate the active queue management (AQM) mechanisms RED In and Out (RIO) and Weighted RED (WRED) in providing levels of drop precedence under different loads. For low drop precedence traffic, FIO and WRED can be configured to offer sheltering (i.e., low drop precedence traffic is protected from losses caused by higher drop precedence traffic). However, if traffic control fails or is inaccurate, such configurations can cause starvation of traffic at high drop precedence levels. Configuring WRED to instead offer relative differentiation can eliminate the risk of starvation. However, WRED cannot, without reconfiguration, both offer sheltering when low drop precedence traffic is properly controlled and avoid starvation at overload of low drop precedence traffic. To achieve this, we propose a new AQM mechanism, WRED with Thresholds (WRT). The benefit of WRT is that, without reconfiguration, it offers sheltering when low drop precedence traffic is properly controlled and relative differentiation otherwise. We present simulations showing that WRT has these properties.