I know for your particular track you may not desire a ringy snare....but, check this out, listen to Track 6, "I Got Two Women:" VH1.com : Sam Lay : Albums: Urge Music Downloads
Or many of the other tracks as well.
A VERY ringy snare. Sometimes sounds almost like an anvil being hit with a hammer!! And, this drummer (Sam Lay) is an incredible blues drummer. He played on many Howlin' Wolf and Muddy Waters records, was in the Paul Butterfield Blues Band, was with Dylan when he unveiled his electric music at the Newport Jazz Festival (Folk Fest.?), AND recorded on Dylan's Highway 61 album (it's his pocket siren on his keychain that you hear on the title track of that album).
VERY ringy snare, but he gets SO MANY sounds out of his snare and has SUCH CONTROL over when it rings and when it doesn't. Kinda hard to hear on these highly-compressed clips, of course, but you can get the idea.
This guy is very much worth checking out, in any case.