We examine the problem of accepting a new request for a pre-stored VBR video stream that has been smoothed using any of the smoothing algorithms found in the literature. The output of these algorithms is a piecewise constant-rate schedule for a Variable Bit-Rate (VBR) stream. The schedule guarantees that the decoder buffer does not overflow or underflow. The problem addressed in this paper is the determination of the minimal time displacement of each new requested VBR stream so that it can be accomodated by the network and/or the video server without overbooking the committed traffic. We prove that this call-admission control problem for multiple requested VBR streams is NP-complete and inapproximable within a constant factor, by reducing it from the VERTEX COLOR problem. We also present a deterministic morphology-sensitive algorithm that calculates the minimal time displacement of a VBR stream request. The complexity of the proposed algorithm make it suitable for real-time determination of the time displacement parameter during the call admission phase.