A technique dynamically resizes Traffic Engineering (TE) Label Switched Paths (LSPs) at a head-end node of the TE-LSPs in preparation to receive redirected traffic in response to an event in a computer network. The novel dynamic TE-LSP resizing technique is based on the detection of an event in the network that could cause traffic destined for one or more other (“remote”) head-end nodes of one or more TE-LSPs to be redirected to an event-detecting (“local”) head-end node of one or more TE-LSPs. An example of such a traffic redirection event is failure of a remote head-end node or failure of any of its TE-LSPs. Specifically, the local head-end node maintains TE-LSP steady state sampling and resizing frequencies to adapt the bandwidth of its TE-LSP(s) to gradual changes in the network over time. Upon detection of an event identifying possible traffic redirection, the local head-end node enters a Fast Resize (FR) state, in which the sampling and resizing frequencies are increased to quickly adapt the TE-LSP bandwidth(s) to any received redirected traffic.