A method, an apparatus and a non-transitory computer-readable storage medium for determining multiple disjoint constrained paths in a communications network are disclosed. The method includes selecting upper bounds QoS metrics for each path in a disjoint combination of paths having two or more disjoint paths between a source node and a destination node; determining a minimum-cost disjoint path combination, and a minimum-QoS metric disjoint path combination; computing a maximum QoS metric by summing the QoS metrics of each minimum-cost path in the minimum-cost disjoint path combination, and computing a minimum QoS metric by summing the QoS metrics of each minimum-QoS metric path in the minimum-QoS metric disjoint path combination.