CRMA-II (Cyclic Reservation Multiple Access, Version II) is a media access control protocol for local and metropolitan area networks working in the Gbit/s range. The access scheme is based on direct access to a slotted medium combined with a reservation scheme guaranteeing both high utilization of network capacity and global fairness. The performance of CRMA-II is improved in comparison with the forerunner CRMA protocol by installing insertion buffers at each station. Network throughput is pushed to values far beyond the transmission capacity by spatial reuse of slots while buffer-insertion technique reduces media access time but increases round-trip delay. In this paper a new media access scheme for Constant Bitrate (CBR) traffic is proposed. For acknowledged CBR connections CBR slots have immediate access to the transmission media. While there is one insertion buffer for each priority of data traffic, CBR traffic is allowed to bypass insertion buffers to ensure minimum delay for constant bitrate services. In this paper a performance evaluation of the CRMA-II media access scheme and the new access mechanism for CBR traffic are presented. The evaluation was done using discrete event driven simulations.