Parsing of argumentative structures has become a very active line of research in recent years. Like discourse parsing or any other natural language task that requires prediction of linguistic structures, most approaches choose to learn a local model and then perform global decoding over the local probability distributions, often imposing constraints that are specific to the task at hand. Specifically for argumentation parsing, two decoding approaches have been recently proposed: Minimum Spanning Trees (MST) and Integer Linear Programming (ILP), following similar trends in discourse parsing. In contrast to discourse parsing though, where trees are not always used as underlying annotation schemes, argumentation structures so far have always been represented with trees. Using the 'argumentative microtext corpus' [in: Argumentation and Reasoned Action: Proceedings of the 1st European Conference on Argumentation, Lisbon 2015 / Vol. 2, College Publications, London, 2016, pp. 801-815] as underlying data and replicating three different decoding mechanisms, in this paper we propose a novel ILP decoder and an extension to our earlier MST work, and then thoroughly compare the approaches. The result is that our new decoder outperforms related work in important respects, and that in general, ILP and MST yield very similar performance.