What value should I increase to reduce noise for subsurface scattering, volume scatter, etc.? I'm on an AMD machine, so GPU rendering is off the table, but I don't mind a lengthy render as long as the end result is good.
So far I've tried:

Rendering at 5000 samples

Various indirect/direct clamp values

Increasing volume sampling max steps

increasing volume bounces (in light paths)
And in all likelihood, a few things I've forgotten.


This render took 40 minutes with tons of settings cranked up, but still has a lot of visible noise despite being fairly small:

I'm using a volume scatter shader to add fog, one transparent plane using a procedural texture for the smoke.
It's worth noting that while I do not have a high-end machine, I also don't have a particularly horrible one either.
You can switch to branched path tracing and use its subsample controls. Increasing subsurface sample level will improve noise for SSS, volumes for volume scatter effects Note that volume samples only affect indirect light, meaning the noise that comes from volume bounces being > 0. For other volume noise, adjust lamp sampling values.

See this question for general info about branched path: What is branched path tracing and how is it useful?

I normally recommend using the "square samples" option with branched path, as it allows you to work with simpler values when juggling all the subsample counts. "square samples" just, well, squares all the values being used for sample counts. So "4" samples becomes 4*4=16 samples. The reason for this is the more samples you have, the more samples you need to add to get a noticeable difference. By adjust sample counts in increments of squares, you ensure you're always getting a statistically significant addition for each sample level.