We present a cost-effective method for obtaining a high-quality annotation of explicit discourse relations in the Czech part of the Prague Czech–English Dependency Treebank, a corpus of almost 50 thousand sentences coming from the Czech translation of the Wall Street Journal part of the Penn Treebank. We use three different sources of information and combine them to obtain the discourse annotation: (i) annotation projection from the Penn Discourse Treebank 3.0, (ii) manual tectogrammatical (deep syntax) representation of sentences of the corpus, and (iii) the Lexicon of Czech Discourse Connectives CzeDLex. After solving as many discrepancies as possible automatically, the final discourse annotation is achieved by manual inspection of the remaining problematic cases. The discourse annotation of the corpus will be available both in the Prague format (on top of tectogrammatical trees) with the Prague taxonomy of discourse types, and in the Penn format (on plain texts) with the Penn Discourse Treebank 3.0 sense taxonomy.