Efficient methods for prediction of minimum free energy (MFE) nucleic secondary structures are widely used, both to better understand structure and function of biological RNA's and to design novel nano-structures. Here, we present a new algorithm for MFE secondary structure prediction, which significantly expands the class of structures that can be handled in O(n^5) time. Our algorithm can handle H-type pseudoknotted structures, kissing hairpins, and chains of four overlapping stems, as well as nested substructures of these types.