The first ATM services are most likely to be constant-bit-rate (CBR) virtual paths (VP) emulating leased-line service. Dealing with static-priority-driven multiplexers at user-network interface, we propose a method to optimally allocate the whole bandwidth of a CBR VP for supporting multiple time-critical traffic. The achievable bandwidth use ratio, with guaranteed quality of service (QoS), is no less than 69% for any combination of time-critical traffic, and can reaches 88% for most of the real scenarii. This method is derived from the rate-monotonic (RM) algorithm which is originally proposed for the scheduling of time-critical tasks. We have proved that the RM algorithm can be applied to the ATM networking, assuming that the admitted traffic sources are loosely-periodic. The RM algorithm can be used by both network operator and user to optimally support a maximum number of time critical traffics on CBR connections. In addition, the use of RM algorithm does not require time-critical sources to be also loss-sensitive, and so supports both time-critical and loss-critical traffic.