This study is a randomized, single-masked controlled trial in which the combination therapy of lithotripsy and the bile acid drug Actigall is compared to monotherapy with only Actigall. The primary objectives are, 1) To determine whether the use of the Medstone STS Lithotripter system in combination with the orally administered drug Actigall is more effective (as measured by percentages of stone free patients 6 months after randomization) in reducing single non-calcified radiolucent gallstones (from 4 to 20mm in diameter) than use of Actigall alone, and 2) To demonstrate that use of the Medstone lithotripsy system is safe (as measured by incidence of adverse events) for the intended purpose, when operated according to its labeling.