A technique efficiently load balances traffic engineering (TE) label switched paths (LSPs) from a head-end node to a tail-end node of a computer network. The novel load balancing technique identifies (e.g., at the head-end node or a path computation element, PCE) a set of paths with equal costs from the head-end node to the tail-end node, where each path of the set is composed of one or more associated links. “Link values” such as, e.g., the number of unconstrained TE-LSPs on the link, the amount of available bandwidth on the link, or the percent of total available bandwidth already in use on the link, are applied to each link of each path. The most restrictive link values (link availability) of each path of the set, such as, e.g., the link with the lowest amount of available bandwidth, etc., are then compared. Upon comparing the link availability, the novel technique load balances established and/or new TE-LSPs from the head-end node to the tail-end node over the set of paths accordingly.