Well I have had a Tilley for years and while it does most of the things that it says on the tin (I have not tried to get an elephant to eat it!!)it is useless in the Mog. The brim is too floppy and merely blows backwards. While I also have a general dislike of baseball caps I have to say that is my most practical and effective solution keeping the sun both off the head and out of the eyes. The trick is to find one that is not too naff.
If I went the flat cap route my kids would never lt me hear the last of it.

Good Luck

Andy
2009 +4 (Finished the service yet Russell?)