We consider streaming of video sequences over both constant and variable bit-rate (VBR) channels. Our goal is to enable decoding of each video unit before exceeding its displaying deadline and, hence, to guarantee successful sequence presentation even if the media rate does not match the channel rate. In this work, we show that the separation between a delay jitter buffer and a decoder buffer is in general suboptimal for VBR video transmitted over VBR channels. We specify the minimum initial delay and the minimum required buffer for a given video stream and a deterministic VBR channel. In addition, we provide some probabilistic statements in case that we observe a random behavior of the channel bit rate. A specific example tailored to wireless video streaming is discussed in greater detail and bounds are derived which allow guaranteeing a certain quality-of-service even for random VBR channels in a wireless environment. Simulation results validate the findings.