Modern data analytics workloads frequently involve complex join queries where the pairwise-join-based algorithms used by most RDBMS engines are suboptimal. In this study, we explore two algorithms that are asymptotically faster than pairwise algorithms for a large class of queries. The first is Yannakakis' classical algorithm for acyclic queries. The second is a more recent algorithm which works for any query and which is optimal with respect to the worst-case size of the output. We introduce a query compiler, DunceCap, which uses these two algorithms and variations on them to produce optimal query plans, and find that these plans can outperform standard RDBMS algorithms as well as simple worst-case optimal algorithms by an order of magnitude on a variety of queries.