Keep in mind that the drum you hear in a recording is the combination of a lot of factors; tuning, head selection, stick selection, player'style/technique, mic selection, mic placement, type of console, engineer and producer's preferences, outboard gear and the amp and transducers (speakers or headphones) you are using to listen. If you walked into the studio where a particular song was recorded, the acoustic drum sound would be quite a bit different than what is being heard in the engineering room. The drums would sound a lot more "live" than you might have expected.
When playing live in a mic'd or more specifically an un-mic'd scenario, it is the overtones that help carry the sound of the drum to the audience. If you deaden a drum to the point where it sounds like Don Henley's snare drum to your ears, by the time it transmits over guitar bass keyboards, horns, strings, the cazoo ensemble and vocals it will sound like a dull "pop."
Over the years, internal mufflers fell out of favor as we all started realizing that they physically work in opposition to the way drum mechanics work. A head is struck and it is depressed downward only to be resisted by a device that pushes upward from underneath in one corner of the head. They work better on snares than other drums as a snare generally does not have much sustain to begin with.
I would suggest adding a bit of external muffling, specifically towards the edge of the drum. You will be surprised how a little goes a long way. If you want to remove almost all if the overtones, something like Zero Rings might be good.
http://www.noblecooley.com/zerorings.html
If you place a Zero Ring on and the drum is too dead, you can always cut and use a percentage of it. A more expensive option would be to try a few different heads and see if that gives you what you want. There are plently of head options out there with muffling built in. The only problem there is it is not adjustable.
What heads are you using currently?