The original idea was to replace the old fashioned way of getting compression - connecting an LDR across the volume control of your amplifier, then illuminating it with an incandescent lamp driven from a tap on the output transformer. The louder the signal, the brighter the lamp, and the more the audio was shunted to earth at the volume control! It was the very simplest compressor, but along with some nice second harmonic distortion introduced by slightly changing the bias voltage to the screen grids of the output bottles, you ended up with a very "loud", very lovely sounding amplifier that would give fabulous sustain to any guitar.
The Really Cheap Compressor is a minimum parts design that was meant to be a replacement for the simple valve amplifier modification outlined above. I've built several of them (which reminds me, I need to make another one this week), and everyone who's used them, likes them. If you use a good quality dual op-amp (a TL072 is OK, but the LM833 or NE5532 are slightly quieter), you won't hear any added hiss, and no added distortion. This compressor is entirely clean, and doesn't have any part of the LEDs (or any other diodes) in the signal path, so there's no clipping (unlike with the rectifier circuit in the Dynacomp). The LDR is slightly slow to respond, so the attack of the guitar note is retained, but the squeeze is nicely applied to the decay portion of the note - just where you want it. This is one of those "is it on?" effects, but you really miss it when it's off!
and a version better suited for bass guitar: