Long-range dependence (LRD) is a largely verified property of Internet traffic, which severely affects queuing performance in network buffers. A common approach for guaranteeing performance requirements is to control the statistical profile of the input traffic by regulators based on the leaky bucket scheme. In this paper, we investigate by simulation how the 1/fα power-law spectrum of LRD traffic is altered when traffic is regulated by a leaky bucket policer. Analysis of the traffic spectral characteristics is carried out mainly by means of the Modified Allan Variance, a time-domain quantity with demonstrated superior accuracy in fractional-noise parameter estimation, recently introduced also for traffic analysis. This approach allows to get a finer insight into power-law spectral characteristics of policed traffic. We also investigate some other properties of the leaky bucket fed with LRD traffic, such as its dropping probability and its effect on queuing delay in a following FI...