Although under my nickname there's Master, I'm more newbie as you probably are, Man! But I have an idea: If you ever know the frequency of these harmonics, a simple frequency filter would erradicate these bad harmonics from the output sound!
If you really don't know what's the frequency, just use variable resistors and change their values accordingly. (For the circuit, I will try on my electric guitar to check for "normal" harmonics, and I'll try to sketch you a simple circuit...)
I hope that's helpful...