p-Cycle reconfiguration methods (for instance complete, incremental, or dynamic-repair) based on the first event adaptive restoration model provide a promising approach for improving the dual-failure restorability characteristics of static p-cycle methods based on the static preplanned restoration model. However, if the reconfiguration process triggered by the first failure is not completed before a second failure occurs, p-cycle reconfiguration methods fail to achieve 100% dual-failure restorability and reduce to the static p-cycle methods which do not take advantage of the spare capacity to be reconfigured. In this study, we propose to use a new restoration model designated as first event locally adaptive restoration model with a coordinated re-restoration effort. This model is aimed to limit the reconfiguration scope to a local p-cycle where the spare capacity is only reconfigured on its straddling links for reducing the reconfiguration overhead (i.e., the average number of reconfigured links during the reconfiguration time.) According to this model, a twophase locally reconfigurable p-cycle method is proposed. Only the straddling links of the local p-cycle affected by the first failure are reconfigured in the first phase. The second phase is not initialized until the second failure really occurs in the affected local p-cycle. The second phase is to enable the dual-failure restorations with a coordinated re-restoration effort for the first failed link from its original end nodes for any damage that the second failure causes to previously deployed restoration paths. The objective of the proposed method is to maximize the dual-failure restorability within a limited reconfiguration scope. We evaluate the correlation between the normalized spare capacity cost and the dualfailure restorability. The results show that the proposed local reconfiguration heuristic method improves the average dualfailure restorability of the 9n17s and Cost 230 networks by 45.1% and 20.1%, respectively, relative to the static p-cycles method and achieves closely the optimal value obtained using integer linear programming (ILP). Additionally, the spare capacity cost of the proposed local reconfiguration method is smaller than that of previous p-cycle reconfiguration methods in the two test networks.