A technique dynamically activates a secondary Traffic Engineering Label Switched Path (TE-LSP) at a secondary head-end node upon failure of a primary TE-LSP in a computer network. According to the novel technique, a primary head-end node establishes the primary TE-LSP having a primary bandwidth (BW) amount to a primary tail-end node. Also, the secondary head-end node establishes the secondary TE-LSP having zero BW to a secondary tail-end node (e.g., the same as the primary tail-end node). The secondary head-end node monitors the state of the primary TE-LSP, and in response to a failure (e.g., or other state change) substantially immediately adjusts the BW of the secondary TE-LSP to the primary BW amount (“activating” the TE-LSP). A “prior-hop” node to the primary and secondary head-end nodes originally forwarding traffic to the primary head-end node, may then begin forwarding traffic to the secondary head-end node, and thus onto the adjusted secondary TE-LSP.