Abstract: A method is disclosed that provides an ordered sequence of reassignments of communications paths to new routes. The network may have multiple excessively long communications paths, referred to as out-of-kilter paths, while other communications paths are of acceptable length, referred to as in-kilter paths. The method approximately optimizes a predefined objective such as maximizing the number of reassigned out-of kilter communications paths. The method may reassign multiple in-kilter paths to new routes in order to free up capacity and allow the reassignment of an out-of-kilter path. Reassignments are executed one at a time according to the ordered sequence determined by the method, and no capacity violations are incurred on any network link at any point in time during the execution of the sequence of reassignments. All reassigned communications paths will be in-kilter.