Link duplication is widely used in Internet protocol networks to tackle the network congestion increase caused by link failure. Network congestion represents the highest link utilization over all the links in the network. Due to capital expenditure constraints, not every link can be duplicated to reduce congestion after a link fails. Giving priority to some selected links makes sense. Meanwhile, traffic routes are determined by link weights that are configured in advance. Therefore, choosing an appropriate set of link weights reduces the number of links that actually need to be duplicated in order to keep a manageable congestion under failure. A manageable congestion is a congestion under which Service Level Agreements can be met. The conventional scheme fixes link weights before determining links to duplicate. In this scheme, the fixed link weights are optimized to minimize the worst network congestion. The worst network congestion is the highest network congestion over all the single non-duplicated link failures. As the selection of links for protection depends on the fixed link weights, some suitable protection patterns, which are not considered with other possible link weights, might be skipped leading to overprotection. The paper proposes a scheme that considers multiple protection scenarios before optimizing link weights in order to reduce the overall number of protected links. Simulation results show that the proposed scheme uses fewer link protections compared to the conventional scheme.