Legacy code can often be made more understandable and maintainable by extracting out selected sets of statements to form procedures and replacing the extracted code with procedure calls. Sets of statements that are non-contiguous and/or include non-local jumps (caused by gotos, breaks, continues, etc.) can be difficult to extract, and usually cause previous automatic-extraction algorithms to fail or to produce poor results. The chief contributions of this paper are a semantics-preserving algorithm for extracting ``difficult'' sets of statements, and a study that compares the algorithm both to an ideal extractor (a human) and to previously reported automatic approaches. We found that ``difficult'' examples do arise frequently in practice, and that our algorithm is a significant improvement over previous work, achieving ideal results over 70% of the time.