This paper deals with the admission of flows with bounded delay and bounded arrivals in a rate-controlled network (more precisely, a network with nodes using ratecontrolled service disciplines with the Earliest Deadline First as the scheduling algorithm). It focuses on an important function of flow admission that has a straight impact on flow admissibility, more precisely, choosing the traffic envelope functions of the rate-controllers traversed by a flow. We present in this paper a method for choosing these envelopes which compared to previous work improves flow admissibility. Then, we show its efficiency through an example.