A technique dynamically splits Traffic Engineering (TE) Label Switched Paths (LSPs) in a computer network. According to the novel technique, a head-end node may determine that a TE-LSP to a destination needs to be sized to a larger bandwidth (a “larger” TE-LSP) than currently available over a single path to the destination (e.g., a path that may also be required to meet other constraints, such as cost, delay, etc.). In response, the head-end node may dynamically “split” the larger TE-LSP, and create a first split TE-LSP over a best (e.g., shortest) available path (e.g., that meets other constraints). The first split TE-LSP may reserve a maximum available bandwidth for that best available path. The head-end node may then continue recursively creating subsequent split TE-LSPs for any remaining bandwidth of the larger TE-LSP over available paths until the larger TE-LSP may no longer be split (e.g., all bandwidth has been placed, configurable maximum number of splits reached, etc.). Notably, the split TE-LSPs may be “re-groomed” at a later time to recombine and reorganize the split TE-LSPs.