It is widely recognized that the maximum number of heavy-tailed flows that can be admitted to a network link, while meeting QoS targets, can be much lower than in the case of markovian flows. In fact, the superposition of heavy-tailed flows shows long range dependence (self-similarity), which has a detrimental impact on network performance. In this paper, we show that long range dependence is significantly reduced when traffic is controlled by a Measurement-Based Admission Control (MBAC) algorithm. Our results appear to suggest that MBAC is a value added tool to improve performance in the presence of self-similar traffic, rather than a mere approximation for traditional (parameter-based) admission control schemes.