This paper investigates an attempt to establish a QoS class that supports long-lived, bulk-data TCP flows that require a minimum rate from the network. The approach is based on a model for TCP flows subject to token bucket marking at the network edge and preferential dropping in the core network. The service class adds admission control functionality and a model for multi-RED queue management to the token bucket marker. The difficulty of parameterizing the mechanisms is discussed and analyzed in an explorative simulation study. A set of configuration parameters that enables a successful operation of the service class is identified and the achievable service provisioning is shown.