Abstract: A gun sound moderator 30 has an external moderator cylinder wall 50 inside which is a series of stages 54 each having a baffle 32 formed with a concentric hole 46 which is concentric with the cylinder wall 50 and a deflector 38, gas passing through the concentric hole being deflected by the deflector 38 so as to move with a radial component towards an end to move with a circulatory motion along/around inside the moderator cylinder wall 30 so as to achieve improved heat transfer from the gas through the moderator cylinder wall and into the ambient atmosphere outside the gun sound moderator so as to achieve cooling of the gas so as to reduce its volume and controlled gas release to atmosphere, so as to achieve a relatively quiet report/noise when a projectile 20 is fired through the gun sound moderator.