1. A Romanian-style haystack, which consists of dried hay stacked upon a bed of tree branches, around a very tall, central pole, and stacked very high.
2. A tarp-covered, Pyramid-framed haystack of my own design.
The disadvantage though, comes when you want to use the hay. As soon as you break the outer shell and remove only some of the hay, the rest of the stack is then vunerable to the weather. Traditionally, all the hay in the whole stack would be hauled away to the barn, or some other form of covered shelter. Another disadvantage is that it has to be constructed in it's entirety at one time. Which means you have to have all your hay ready at one time (which takes a tremendous amount of hay), because the hay itself needs to be shaped and combed to become the "roof". With my Pyramid haystack, you can keep adding hay over time as it's ready, because it's "roof" is a removable tarp.
If you want to learn about the Romanian style of haystack, there are excellent pictorials at http://www.hayinart.com/003028.html and
http://leafpile.com/TravelLog/Romania/Farming/MakingaHaystack/MakingHaystack.htm . The people at Leaf Pile, are also publishing a photobook with essays on the rural life of Northern Transylvania, called "The Color of Hay: the Peasants of the Maramures" . It will be available in October 2010. You can order it at http://colorofhay.com/
A picture is worth a thousand words!