Less-configurational languages such as German often show not just morphological variation but also free word order and nonprojectivity. German is not exceptional in this regard, as other morphologically-rich languages such as Czech, Tamil or Greek, offer similar challenges that make context-free constituent parsing less attractive. Advocates of dependency parsing have long pointed out that the free(r) word order and non-projective phenomena are handled in a more straightforward way by dependency parsing. How-ever, certain other phenomena in language, such as gapping, ellipses or verbless sentences, are difficult to handle in a dependency formalism. In this paper, we show that parsing of discontinuous constituents can be achieved using easy-first parsing with online reordering, an approach that previously has only been used for dependencies, and that the approach yields very fast parsing with reasonably accurate results that are close to the state of the art, surpassing existing results that use treebank grammars. We also investigate the question whether phenomena where dependency representations may be problematic – in particular, verbless clauses – can be handled by this model. 1