The main function of a compressor is to reduce dynamic range. They're not just used to increase perceived volume so you can achieve the loudest CD on the planet. That's in itself is worth remembering.
Most have a make-up gain/volume knob. The most common setting is to have the compressor set to reduce the volume above the threshold, resulting in the peaks being levelled out. That reduces the overall volume of the signal, so the make-up gain is increased to "make-up" the difference.
You can also increase the make-up gain beyond that to end up with an even louder signal.
Turn it Down
But it works the other way around as well. Turn the make-up gain down below the level of the incoming signal.
Now for mixing, turning it down isn't that useful. You can always use a gain plug-in or better still ride/automate the faders. Actually, that's a general rule: if you just want to change the volume of a channel, use the faders, not a compressor.
But for live use or for recording a guitarist, the compressor's volume/gain knob is useful for reducing the output signal from a guitar as well as increasing it. It does have other characteristics though, although they add a good quality to the sound.
From a guitarist's perspective
It starts with the setting of the clean channel on a valve amp. You mileage may vary with solid-state/hybrid amps, some are better at tube emulation than others. At least try one that uses a tube preamp.
1) To move into distortion

2) To clean up the sound

It's not just a question of volume
The compressor is not being used solely as a boost/cut for the volume. If I wanted just a volume change, then I'd use a boost pedal or a volume pedal. If I've set the output signal closely enough to the input level, then the guitar's signal still comes through, in a reduced dynamic range, but close to the original volume of the guitar. By doing it that way, I can get a nice and usable variety in the tone, either moving into or out of the break-up range of the amplifier.
Why not use the guitar's volume knob?
This depends on the guitar. On most of mine, reducing the volume knob even by a fraction cuts the treble output from the guitar more than the middle or lower frequencies. I do use it to regulate volume and tone but I'm aware of the skewed effect it has on eq.
Part of a series by Award Sounds offering a selection of creative ideas to kick-start or rejuvenate a composition.