A suppressor for a firearm includes a first gas expansion section of relatively large size sufficient to reduce the temperature and pressure of the gas expelled from a muzzle during discharge of the firearm to a level that avoids rapid degrading of structural members such as baffles in the suppressor that are downstream of the muzzle. The gas is channeled through multiple paths to distribute its energy more equally. Preferably, the suppressor is formed with a lightweight, thermally-conductive composite portion. The composite portion provides lightweight, bursting strength with good thermal conductivity and little contribution to vibrational instability of the muzzle to which it is attached. The composite portion may be of a carbon fiber, silicon, boron, or metallic base. In one embodiment, a first expansion chamber is in communication with the muzzle and with a second expansion chamber and in another embodiment, the first expansion chamber communicates with the muzzle and with the second expansion chamber The composite portions of the suppressor provide good bursting strength and heat conductivity with light weight. In some embodiments, a series of baffles creates turbulence in the gas, slowing its motion and distributing the energy more evenly over space.