338 Lapua Suppressor

You might try running a search or otherwise having a read through some of the "Suppressors" sub-forum for more on this topic (and perhaps ask a Mod to move this thread there for you as it'll likely get more traffic there too).
 
Shorter barrel = higher muzzle pressure

Some cans aren't rated for the higher pressures you get with short .338LM barrel, but that's mostly in the 16-18" range.
 
I have had outstanding success with the Elite Iron Sierra thread-on http://eliteiron.com/elite-iron-suppressors-page6b.htmlshared between my .308/.338LPM DTA srs. The thread on format has been very consistant vs. any of the 4 AAC 18-51 tooth rifle cans I have been using. It has a repeatable 4MOA vertical POI shift-presumably from flexing the barrel. One of the RM's at a recent PR match commented that it was quieter (on the .308) than any of the other shooters dedicated .308 cans. That being said it is somewhat heavy. Dale at Elite Iron sent me a "timing wheel" prior to producing my can so that the internal baffles were precisely aligned horizontally. I think I ended up at 1500 w/o NFA tax, and they had it built and to my dealer in 8 weeks. Hope this helps. Walt
 
Suppressed Armament Systems: Vengeance Titanium Suppressor, I use it on my 338 Lapua and my 308. The 308 has a longer barrel compared to the 338 so POI shift is 4 inches low when I put it on the 308. The 338 I get 1 inch of MOA when I attach it and I have had no issues. A shorter and thicker barrel makes less of a POI shift compared to a longer barrel, yes it is a suppressor but its nick name should be barrel weight which changes the harmonics of the barrel.