A method and apparatus for performing a dynamically runtime adjustable constrained shortest path first (CSPF) computation of a label switched path (LSP) is described. In one embodiment of the invention, a network element acting as a source of the LSP receives a request to compute the LSP which includes one or more traffic engineering constraints. If the request includes at least one additive constraint, the network element performs a CSPF calculation. If the request does not include an additive constraint, the network element prunes each link that does not satisfy each of the constraints, and prunes those links whose paths converge at an intermediary network element according to cost, calculates a path to the destination according to cost. Other methods and apparatuses are also described.