For a hard case, it is difficult to beat the DLX Take-Down Recurve Travel Case. It works great for 3 piece longbows too, and even for many 2 piece longbows. It has a 6 inch diameter and can even hold arrows up to about 30.5" without points or broadheads. The Safari Tuff soft cases are great too if you don't need the protection of a hard case. I have the Rhino cases and the Gazelle cases. The Gazelle cases are a little more protective, but the Rhino cases fold out and give you some flexibility for uses that the Gazelle will not accommodate. Any of the cases will fit in a 36" duffle bag. When flying on an airline with my checked luggage being a duffle bag, I always use my 3 Rivers DLX Take-Down Recurve Travel Case. I don't trust the airlines not to damage a bow in a soft case unless the soft case is packed in hard-sided baggage.
Allan