Statistical multiplexing of video contents aims at transmitting several variable bit rate (VBR) encoded video streams over a band-limited channel. Rate-distortion (RD) models for the encoded streams are often used to control the video encoders. Buffering at the output of encoders is one of the several techniques used to smooth out the fluctuating bit rate of compressed video due to variations in the activity of video contents. In this paper, a statistical multiplexer is proposed where a closed-loop control of both video encoders and buffers is performed jointly. First, a predictive joint video encoder controller accounting for minimum quality, fairness, and smoothness constraints is considered. Second, all buffers are controlled simultaneously to regulate the buffering delays. This delay is adjusted according to a reference delay constraint. The main idea is to update the encoding rate for each video unit according to the average level of the buffers, to maximize the quality of each program and effectively use the available channel rate. Simulation results show that the proposed scheme yields a smooth and fair video quality among programs thanks to the predictive control. A similar buffering delay for all programs and an efficient use of the available channel rate are ensured thanks to the buffer management and to the predictive closed-loop control.