We revisit the join ordering problem in query optimization. The standard exact algorithm, DPccp, has a worst-case running time of $O(3^n)$. This is prohibitively expensive for large queries, which are not that uncommon anymore. We develop a new algorithmic framework based on subset convolution. DPconv achieves a super-polynomial speedup over DPccp, breaking the $O(3^n)$ time-barrier for the first time. We show that the instantiation of our framework for the $C_\max$ cost function is up to 30x faster than DPccp for large clique queries.