On organic shapes, UV mapping is a bit of work. In the tutorial series I created, I covered UVs and unwraps plus a bunch of other tricks. 

The UV unwrap will do everything at once, repositioning content as if it's still attached, and won't individually remap areas that have had the polygon detach done to them. The detach feature, instead, allows you to grab the polygons and manually reorient them. (make sure you save the polygons with a selection name so you can use the "select by name" function) This way, to be simple, if you had a cowboy had, you could manually select the brim and to a parametric display for that, and on the same UV sheet, then do a cylinder wrap/display for the  part of the hat that is left. 

Clear as mud?