Shaped or suitcase configured? All storage on the inside or is outside OK? Something to carry back-pack style or does it matter. It all depends on what you're looking for. More details would be nice because there are a lot of cases out there. Practically any case will fit a III.
Just go to wwbw.com, finecases.com, pmwoodwind.com, etc. If you want more pockets, get a ProTec, if you want more room inside than your BAM /Selmer case and with outstanding protectiveness, get a Hiscox. I personally like the Selmer Ref case I have for my alto. I bought it "used" but as good as new at a fair price from a forum member, so just because a case is Selmer, don't overlook used/good as new cases.
When all else fails, look in the Cases area of the forum and/or google "Saxophone cases" .
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