Drums will always resonate bai and there will always be overtones bisag unsaon nimo. Remember - drum sounds from recorded tracks are gated and processed so ayaw i-compare ang imong live sound diha sa madunggan nimo sa imong CD. Also - piccolo snares have less shell surface which translates to less resonation... so gamay ra gyud ang overtone.
The overtones from your snare drum shouldn't be that much. First off, you're using a Mahogany-Poplar drum shell which doesn't resonate much... and the Remo Emperors are double-ply. Try tuning the resonant side medium to medium low... then tune your batter side to medium. That would keep the overtones to a minimum but would produce a wet and fat sound.. dunno if you want that.
If you want to get rid of your overtones completely (which I don't really recommend since you're killing the drum's natural sound), you can make O-RINGS out of your old drumhead and mount it on top of your snare drum.
