The term "Clean Up" of guitar effects is in most cases related to Fuzz Face or (Treble) Booster type of effects. This section will explain the technique and technical background of this so called "Clean Up" using a Fuzz Face.
Jimi Hendrix is one of the first using this technique getting various sound characters with using a Dallas Arbiter Fuzz Face, germanium transistor version, and a Sound City and/or Marshall amp. You can hear the clean up effect on the album Axis: Bold as Love released at the end of 1967. His sound going from transparant clean chord picking sound to a thick bassy solo sound.
Jimi created this sound by using an early version Dallas Arbiter Fuzz Face, in combination with an Sound City and/or Marshall amp and a standard Fender Stratocaster.
The technique to get this clean up sound is setting your amp on clean or very light crunch, old Sound City and Marshall amps only had one clean channel and distorted only at high volume or using boost pedals. In this setting, with the Fuzz Face engaged, turning down the volume on your guitar to about 5 or 6 will give a clean up without loosing significant volume.
The following scope pictures show the clean up effect. The lower signal is representing the input signal of the Fuzz Face and corresponds to a guitar signal level. The upper signal is the resulting fuzz face ouput.
Guitar volume on 10, a fuzzy, distorted sound with a lot of bass content. Can be farthy and compressed making chords muddy. Mostly used for single note solo's.
Guitar volume on about 8 to 9, a distortion sound with reduced bass content. Resulting in a dynamic distortion reacting very good on your playing dynamics and chords having a good single note definition. The early ZZ top sound of Billy Gibbons was based on this principle.
Guitar volume on about 6 to 8, a crunch sound with reduced bass content. Resulting in a dynamic crunch sound and again reacting very good on your playing dynamics.
Guitar volume on about 5 to 6, a clean transparent sound. Resulting in trebly clean sound without loosing dynamics and significant volume.