We describe experiments in parsing the German TIGER Treebank. In parsing the complete treebank, 86.44% of the sentences receive full parses; 13.56% receive fragment parses. We discuss the methods used to enhance coverage and parsing quality and we present an evaluation on a gold standard, to our knowledge the first one for a deep grammar of German. Considering the selection performed by our current version of a stochastic disambiguation component, we achieve an f-score of 84.2%, the upper and lower bounds being 87.4% and 82.3% respectively.