The answer depends on what you mean by the 'old' and the 'new' stress system, i.e. if you actually mean the stress system changes made in 0.40.X, or you're actually asking about the new needs system introduced in 0.42.X. I'm assuming you're actually asking about the stress below.
The updated 0.40.X stress system, which is still present in 0.42.X, has stress built up by bad things, and stress reduced by nice things, such as good bedrooms, nice drinks, etc. That includes mist generators (which I've never built), but the most important part is to keep sapient body parts out of the view of your dorfs. These body parts ought to be destroyed or dumped into a hole deep enough so haulers don't see the remains at the bottom of the hole. Each season any part of a sapient body is seen it will produce a new negative thought, but only once per creature and season. Vengeful thoughts brought on by annoying birds are hard to control, and can easily cause a breakdown on themselves, since they spiral out of control. The best thing in these cases is probably to get your dorfs indoors out of reach of the pests.
In 0.42.X it seems dwarven sensitivity to sapient body parts has been reduced, so some dorfs can see body parts without being horrified, while others still are affected. If any dorf starts to get stressed out, that dorf ought to be taken off corpse hauling duty (note that sapient bodies are corpses in 0.42.X, not refuse [excluding dwarven remains], as in 0.40.X).