I just figured out why you might want a slower compressor like an LA-2A first, and then a faster one like an 1176 second, when recording something like bass guitar. I'd long assumed it should be the other way around.
I'm slow, but I do get there eventually.
For anybody who finds it as counterintuitive as I did: the idea is to get the main part of your playing to a relatively consistent level including the transients, and then level out all the transients in one pass.
Edited to add better explanation: as your playing varies in level, so do your transients. It's difficult to build a compressor that will figure out what the threshold should have been, for each note.
A slower compressor ignores the transients and brings the rest of the signal to a more consistent level, and the transients come along for the ride. Now it's much easier to level them out.
In hindsight, this is so obvious as to be physically painful, but welcome to my life.