We consider the transmission of variable bit rate (VBR) video over a network offering a guaranteed service such as ATM VBR or the guaranteed service of the IETF. The guaranteed service requires that the flow accepted by the network has to be conforming with a traffic envelope \sigma; in return, it receives a service guarantee expressed by a network service curve \beta. Functions \sigma and \beta are derived from the parameters used for setting up the reservation, for example, from the T-SPEC and R-SPEC fields used with the Resource Reservation Protocol (RSVP). In order to satisfy the traffic envelope constraint, the output of the encoder is fed to a smoother, possibly with some look-ahead. The resulting stream is transported by the network; at the destination, the decoder waits for an initial \emph{playback delay} and reads the stream from the receive buffer. We consider the problem of whether there exists one optimal strategy at the smoother which minimizes the playback delay and the receive buffer size, given the traffic envelope \sigma and the service curve \beta. We show that there does exist such an optimal smoothing, and give an explicit representation for it. We also obtain a simple expression for the smallest playback delay and playback buffer size which can be achieved over all possible smoothing and playback strategies. We show that the computation of optimal smoothing and minimum playback delay do not depend on the past. We show that separate delay equalization is optimal in the CBR case, but not otherwise. We also apply the theory to the analysis of which T-SPEC should be requested by a source-destination pair, given some playback delay and buffer constraint, and given the path characteristics advertised in RSVP PATH messages.