rays get stuck due to total internal reflection back

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(L) [2012/11/04] [tby guo] [rays get stuck due to total internal reflection] Wayback!

Hi there,
I implemented the ideal dielectric reflection and refraction BSDF, then rendered this glass of water with maximum ray bounces being limited to 16:
[IMG #1 Image]
As we can see, those dark edges correspond to rays which suffer from many many specular bounces before escaping that glass.
Since such paths are deterministic though deep, is there any analytical way to sample more efficiently?
Many thanks for your precious suggestions.
Regards,
Guo
[IMG #1]:Not scraped: https://web.archive.org/web/20161005163406im_/http://i1339.photobucket.com/albums/o713/guozhou/glass.png

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