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We conducted a case study of parallelizing a real program for multicore computers using currently available libraries and tools. We selected the sequential Bzip2 compression program for the study because it's a computing-intensive, widely used, and relevant application in everyday life. Its source code is available, and its algorithm is well documented. In addition, the algorithm is non-trivial, but, with 8,000 LOC, the application is small enough to manage in a course.