Several distributed real-time applications (e.g., medical imaging, air traffic control, and video conferencing) demand hard guarantees on the message delivery latency and the recovery delay from component failures. As these demands cannot be met in traditional datagram services, special schemes have been proposed to provide timely recovery for real-time communications in multihop networks. These schemes reserve additional network resources (spare resources) a priori along a backup channel that is disjoint with the primary. Upon a failure in the primary channel, its backup is activated, making the real-time connection dependable. In this paper, we propose a new method of providing backups called segmented backups, in which backup paths are provided for partial segments of the primary path rather than for its entire length, as is done in the existing schemes. We show that our method offers: 1) improved network resource utilization; 2) higher average call acceptance rate; 3) better quality-of-service guarantees on propagation delays and failure-recovery times; and 4) increased flexibility to control the level of fault tolerance of each connection separately. We provide an algorithm for routing the segmented backups and prove its optimality with respect to spare resource reservation. We detail necessary extensions to resource reservation protocol (RSVP) to support our scheme and argue that they increase the implementation complexity of RSVP minimally. Our simulation studies on various network topologies demonstrate that spare resource aggregation methods such as backup multiplexing are more effective when applied to our scheme than to earlier schemes.