Standard phrase-based statistical machine translation systems generate translations based on an inventory of continuous bilingual phrases. In this work, we extend a phrase-based decoder with the ability to make use of phrases that are discontinuous in the source part. Our dynamic programming beam search algorithm supports separate pruning of coverage hypotheses per cardinality and of lexical hypotheses per coverage, as well as coverage constraints that impose restrictions on the possible reorderings. In addition to investigating these aspects, which are related to the decoding procedure, we also concentrate our attention on the question of how to obtain source-side discontinuous phrases from parallel training data. Two approaches (hierarchical and discontinuous extraction) are presented and compared. On a large-scale Chinese!English translation task, we conduct a thorough empirical evaluation in order to study a number of system configurations with source-side discontinuous phrases, and to compare them to setups which employ continuous phrases only.