All interesting suggestions, but here's the quick, easy, unexpected answer.
Cut out a 13½" circle from a new 14" head. Tune the snare higher than you think it should be. Not 311 or No Doubt high, but med-high to retain some definition and attack. Then place the cutout on the batter. Pitch will drop, sound gets wet, you even get a little gate to it. Works on 5-6½" deep snares the best.
This is an old studio secret, a sound you cannot get with any other kind of damping - wallets, rings, gel, tape, towels, doesn't matter.
If you tune the drum way down, and use the overlay, the sound is just wet and sloppy and cool (think Bev Bevan and E.L.O.) You will never get that with any other head or damping combination.
Have fun!
Bermuda
* Note, you should use a 1-ply head as the overlay, coated or clear is fine. Also works wonders on toms!