I just wanted to share this because it's been surprisingly helpful in correcting my swayback...I have a huge amount of hyperflexibility in my lower back (partially from gymnastics, partially just anatomy) so of course I get HAMMERED in any dance class I take. It sometimes seems really unfair because I see other students with terrible posture, who slouch, who have hyperextended knees, who are over turned-out, and yet the teacher ignores them and just keeps griping about my arched back as if that were the only thing that mattered.
ANYWAY! heh...well, we got a new jazz teacher the other day and one of the first things she told me was to concentrate on pushing my ribcage back, in addition to just tucking my pelvis under. Normally all I ever get is "Tuck your pelvis, tuck your pelvis," so I tried the ribcage thing - and wow, I really noticed a difference. It really helped to be able to see the correction coming from two distinct parts of the body - I think a lot of times people with swayback are also centered a little forward, so bringing the ribcage back helps correct that as well.
Anyway I'm babbling, just thought that was interesting.