In this paper, we studied the traffic smoothing and bandwidth allocation issues for VBR MPEG-2 video connections in ATM networks. First of all, the statistical characteristics of VBR MPEG-2 video sequences were examined by real observation. The obtained results showed that it would be very difficult to efficiently allocate an appropriate amount of bandwidth if such traffic were straightforwardly feed into the network. We therefore introduced a so called macro-frame (M-frame) smoothing scheme. It was found that the smoothed traffic not only possesses relatively simple characteristics but also makes the bandwidth allocation more efficient. In consideration of that there is not yet a proper bandwidth allocation algorithm for VBR MPEG-2 connections, we examined and compared the simple peak rate allocation and Gaussian approximation. It was found that 1) peak rate allocation is far more inefficient than the actual need and 2) Gaussian approximation is surprisingly accurate and efficient in estimating the bandwidth, especially in smoothed traffic case.