Abstract: We introduce a novel chart-based algorithm for span-based parsing of discontinuous constituency trees of block degree two, including ill-nested structures. In particular, we show that we can build variants of our parser with smaller search spaces and time complexities ranging from O(n^6) down to O(n^3). The cubic time variant covers 98% of constituents observed in linguistic treebanks while having the same complexity as continuous constituency parsers. We evaluate our approach on German and English treebanks (Negra, Tiger, and DPTB) and report state-of-the-art results in the fully supervised setting. We also experiment with pre-trained word embeddings and Bert-based neural networks.