Well, my basic "clean" tone is actually lightly overdriven as well, partially from a Joyo Orange Juice, placed towards the very beginning of my signal chain, set to a relatively low gain overdrive and blended with about 40% or so clean signal, via one of my Boss LS-2 pedals, and partially from my tube preamp, placed towards the very end of my signal chain, having the input gain control turned up to the point where the tubes just starts to break up lightly.
But unlike you I very much like the growl that adds to my low end.
As to how to keep the low end clean you got two options:
- Either you place whatever overdrive you use in one of the effects loops of for instance a Boss LS-2, but with a HPF pedal in the same effects loop stacked into your overdrive, that way making sure to only overdrive the upper frequency spectrum of your signal, accordingly to how you got the HPF set, and then blend in the full clean signal from the other empty effects loop of the LS-2, including the low end that you cut out from the overdriven signal.
- Or you get an effects loop pedal/switcher with a build in crossover, allowing you to dial in which part of the frequency spectrum goes to your overdrive and which part to your clean signal.
I know for certain such pedals does in fact exist, but unfortunately any specific name escaped me at the moment, so you'll have to do a Google search yourself, or wait for other to chime in with more specific names on which options you got to chose from for this solution.