Video applications are expected to generate a significant proportion of the traffic in the future B-ISDN. We consider the different possibilities for the transport of video signals provided by the service classes defined by the ATM Forum and the ITU-T, focusing attention on preventive rather than reactive control. The options available for statistical resource sharing are discussed in terms of Rate Envelope Multiplexing (REM) and Rate Sharing (RS). We analyse the characteristics of the output of video coders and argue for burstiness reduction using rate shaping inside the coder to facilitate traffic control. The adequacy of REM and RS for multiplexing VBR video connections in ATM is compared through quantitative performance evaluations.