We present a novel selection algorithm for N-2 contingency analysis problem. The algorithm is based on the iterative bounding of line outage distribution factors and successive pruning of the set of contingency pair candidates. The selection procedure is non-heuristic, and is certified to identify all events that lead to thermal constraints violations in DC approximation. The complexity of the algorithm is O(N[superscript 2]) comparable to the complexity of N-1 contingency problem. We validate and test the algorithm on the Polish grid network with around 3000 lines. For this test case two iterations of the pruning procedure reduce the total number of candidate pairs by a factor of almost 1000 from 5 millions line pairs to only 6128.National Science Foundation (U.S.) (Award ECCS-1128437)MIT Skoltech Initiative (Seed Funding Grant)Russian Government Contract (11.519.11.6018)