I agree with Mr D above, sounds like transistor clipping to me, especially since you use the word crackling. Transistor amplification always has a threshold at which this clipping (bad, ugy, crackly distortion) will occur. That is one of the advantages to tube amps - they don't have an absolute threshold of clipping like transistor devices, they compress and distort in a pleasing way. Very possibly the distorto pedal you are using compresses the signal enough so that it doesn't clip the amp, so the clipping only occurs with the clean sound. Here's some ideas fer u:
I just bought a Danelectro 7 band eq pedal for $30. (+tax) at Guitar Center - in addition to tweaking the eq a little, I use its level control to compensate for the signal strength on different guitars thru my live rig. With my stock Strat, I raise the volume about 3 db above the center detent (boost), with my medium output humbucker guitar I lower the slider about 3 db below the detent to cut the signal. You could set this up to cut your signal a little for the clean, with the added benefit of having more control over the eq.
Lower the gain on the amp's input to where it doesn't clip for your clean tone, and turn up the level on the distorto pedal for that sound.
Find a cheap (one that fits your budget) compressor pedal, set the compressor to limit/compress your clean tone to where it won't clip, and yet isn't too compressed sounding and switch it on only for your clean setting. With a SS amp, you might consider this an improvement in its sound anyway.
What kind/model amp is it?