A technique avoids unnecessary preemption of resource reservations along a requested flow between nodes in a computer network. A node receives priority-based resource reservation requests and determines conditions of reservation eligibility by comparing the requested resources to the amount of available resources at the node. Specifically, the node maintains a “held resources” state where available requested resources are held prior to their being assigned or reserved (confirmed) for the requested flow, such as, e.g., during an initial Resource reSerVation Protocol (RSVP) Path message. The node includes the held resources in calculations of available resources in such a way as to prevent resources from being assigned or reserved if the resources would be subsequently preempted by a request of higher priority, or if an earlier request would first utilize the resources. The node (e.g., an end node) also prevents resources from being reserved or preempted in a duplex (bi-directional) reservation on a first flow in a first direction when resources available for a second flow in a second direction indicate a failure of the second flow.