I noticed AgonSwim has a new brief called Brief 2.0 (they still sell the old Briefs) It is only made in Lycra though. The standard Brief (call it 1.0) is available in many fabrics except Lycra. Their Euro brief (smaller sides) is still made too with different fabrics. I can't tell how it's different from the photos. If you had bought the new ones, let us know what it's like.
http://www.agonswim.com/