The use of fiber metal or similarly high flow resistance and high acoustic transparency material as a liner for traditional acoustically absorptive media in a dissipative muffler exhibits improved low frequency sound attenuation, reduces backpressure, and eliminates media entrainment or "blow-out" phenomenon which results in longer muffler life. The same class of materials may also be used to fashion an element that provides linear occlusion inside an otherwise line-of-sight type of muffler, where the occluding element provides improved impedance-matching acoustic absorption. Disclosed embodiments providing linear occlusion minimize traditional increases in muffler backpressure by incorporating helical, conical, and annular members in mufflers with round ducts. To maximize attenuation, a muffler according to the invention may feature both a fiber metal fill liner and a fiber metal linear occlusion element. Further, the liner that connects the inlet and outlet ports of the muffler may feature an offset, elbow, or turn that would simultaneously allow it to provide means for linear occlusion.