Techniques are described for reusing downstream-assigned labels when establishing a new instance of a label switched path (LSP) prior to tearing down an existing instance of the LSP using make-before-break (MBB) procedures for RSVP. The techniques enable a routing engine of any non-ingress router along a path of the new LSP instance to reuse a previously allocated label for the existing LSP instance as the downstream assigned label for the new LSP instance when the paths of the existing LSP instance and the new LSP instance overlap. In this way, the non-ingress router does not need to update a label route in its forwarding plane for the reused label. When the new LSP instance completely overlaps the existing LSP instance, an ingress router of the LSP may avoid updating an ingress route in its forwarding plane for applications that use the LSP.