A method comprising: computing, by an ingress router, a plurality of paths for a plurality of sub-label-switched paths, sub-LSPs, from the ingress router to an egress router, of a multi-path label-switched path, MP-LSP, wherein computing the plurality of paths comprises determining, for a common transit router included as a hop in each of the plurality of sub-LSPs, a plurality of incoming per-hop bandwidth constraints for the plurality of paths and a plurality of outgoing per-hop bandwidth constraints for the plurality of paths, wherein a sum of a quantity of bandwidth to be reserved by the plurality of incoming per-hop bandwidth constraints corresponds to a sum of a quantity of bandwidth to be reserved by the plurality of outgoing per-hop bandwidth constraints, and wherein, for each path of the plurality of paths, a respective incoming per-hop bandwidth constraint of the plurality of incoming per-hop bandwidth constraints has a different value than a respective outgoing per-hop bandwidth constraint of the plurality of outgoing per-hop bandwidth constraints; and outputting, by the ingress router, for each path of the plurality of paths, a respective resource reservation request message to establish a respective sub-LSP (18A, 18B), from the ingress router to the egress router, of the plurality of sub-LSPs, each respective resource reservation request message including an indication of an explicit route, a tunnel identifier indicating the MP-LSP, an identifier for the respective sub-LSP, an indication of a per-hop bandwidth constraint that corresponds to a respective incoming per-hop bandwidth constraint of the plurality of incoming per-hop bandwidth constraints, and one or more instructions to modify the indication of the per-hop bandwidth constraint, the one or more instructions including an instruction to modify the indication of the per-hop bandwidth constraint at the common transit router to correspond to a respective outgoing per-hop bandwidth constraint of the plurality of outgoing per-hop bandwidth constraints. computing, by an ingress router, a plurality of paths for a plurality of sub-label-switched paths, sub-LSPs, from the ingress router to an egress router, of a multi-path label-switched path, MP-LSP, wherein computing the plurality of paths comprises determining, for a common transit router included as a hop in each of the plurality of sub-LSPs, a plurality of incoming per-hop bandwidth constraints for the plurality of paths and a plurality of outgoing per-hop bandwidth constraints for the plurality of paths, wherein a sum of a quantity of bandwidth to be reserved by the plurality of incoming per-hop bandwidth constraints corresponds to a sum of a quantity of bandwidth to be reserved by the plurality of outgoing per-hop bandwidth constraints, and wherein, for each path of the plurality of paths, a respective incoming per-hop bandwidth constraint of the plurality of incoming per-hop bandwidth constraints has a different value than a respective outgoing per-hop bandwidth constraint of the plurality of outgoing per-hop bandwidth constraints; and outputting, by the ingress router, for each path of the plurality of paths, a respective resource reservation request message to establish a respective sub-LSP (18A, 18B), from the ingress router to the egress router, of the plurality of sub-LSPs, each respective resource reservation request message including an indication of an explicit route, a tunnel identifier indicating the MP-LSP, an identifier for the respective sub-LSP, an indication of a per-hop bandwidth constraint that corresponds to a respective incoming per-hop bandwidth constraint of the plurality of incoming per-hop bandwidth constraints, and one or more instructions to modify the indication of the per-hop bandwidth constraint, the one or more instructions including an instruction to modify the indication of the per-hop bandwidth constraint at the common transit router to correspond to a respective outgoing per-hop bandwidth constraint of the plurality of outgoing per-hop bandwidth constraints.