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 this context, the output of the video encoder is constrained by the traffic envelope defined at the network entry point, the playback delay budget and the decoding buffer size. In previous works, the constraints are satisfied either by smoothing a fixed coder output, or by modifying the encoding parameters. In this paper we take a combined approach. This allows us to find a joint source rate selection/smoothing solution which minimizes the total average distortion while satisfying constraints on traffic envelope, playback delay and decoding buffer size. Our solution is based on a Viterbi-like algorithm. Our approach is made possible by the representation of the optimally smoothed output as the time inverse of a shaper output. Preliminary experimental results exhibit significant improvements in terms of total average distortion compared to the Open-Loop VBR case, under equivalent traffic parameters and decoding constraints.