I know there's at least one model of compass that lets you set declination (difference between magnetic and true north) by manually adjusting the position of the central capsule and the outer, graduated ring.

The adjustment is done manually -- not with a screw. One holds the capsule still and rotates the outer ring until the desired declination is set.

Can anyone help me figure out which compass this is?

Bear

I know the Brunton Eclipse models work that way. I am sure there are others.

The Brunton model 9020 works that way, as does the model 8099 (the Eclipse, which was already mentioned)

I've got a couple cheap Bruntons that work that way, and have done me good.

Brunton 8096AR also does this.

But let me add, this is not a negative on the product. I set my dec. on the 8096 and have carried it for months without a tick off angle.

The Silva models have a screw adjustment. Many others do to. Perhaps this gives the user more confidence, I am confident in both.