It was demonstrated that a bypass duct similar to a Herschel- Quincke tube could be used to increase the transmission loss of mufflers at selected frequencies. In many cases, the duct can be short and thought of as a leak. It was shown that the optimal length and cross-sectional area could be determined by using a simple optimization technique known as the Vincent Circle. Most importantly, it was demonstrated that the attenuation at low frequencies could be improved by as much as 15 dB. To prove the concept, a muffler was designed and optimized using transfer matrix theory. Then, the optimized muffler was constructed and the transmission loss measured using the two-load method. The measured results compared well with prediction from transfer matrix theory. Boundary element simulation was then used to further study the attenuation mechanism.