When the volume pot is lowered from ’10’, resistance is added in series with the signal output of the pickup. This resistance, combined with the cable capacitance, and the pickup itself forms a low pass filter, allowing lower frequencies through but blocking some of the higher frequencies. The resultant tone for most people becomes unusable.
There is a simple and very cheap fix for this problem, and it is well worth doing. The solution is to install a treble bleed circuit to your guitar, which can be either a single capacitor or a combination of a capacitor and a small resistor. A capacitor wired in parallel with the terminals on your volume pot will allow the high frequencies through when the volume is reduced. The capacitance value of the capacitor will determine the cut off point for the frequencies allowed through. Wiring a resistor in series or parallel with the capacitor will help to control the brightness. To install this circuit yourself you will need some basic tools, a soldering iron, solder, the necessary components and the confidence to use them. If you are not confident in performing your own guitar modifications, any guitar tech should be able to do this.