Exemplary traffic engineering solutions are described herein. According to exemplary embodiments, multiple tiered thresholds representing allocatable capacities of links in the network may be provided. The tiered thresholds may effectively limit the amount of data that a traffic engineering system is permitted to allocate on links in the network. The traffic engineering system may attempt to allocate data flows in the network according to the smallest threshold. If the network cannot accommodate the data flows according to the smallest threshold, then the next-smallest threshold may be attempted. The thresholds may be sequentially tested in increasing order until the largest threshold is attempted. If a workable threshold is found, then the data flow may be allocated to a path in the network. If the traffic engineering system is unable to accommodate the data flows at any of the tiered thresholds, then the traffic engineering system may report a failure.