I think I've found a compromise!
The picture to the left there is a fence most often seen in Newfoundland, Canada. It's called a variety of names, Riggle, Wriggle, Riddle ... and it's bloody hard to find any info on the web! The Heritage Foundation of Newfoundland & Labrador has this to say,
"The riggle rod (wriggle, riddle, lear, roddle) fence is the most unique fence type in Newfoundland and it is very rare today. It is a combination of a longer fence and a picket fence and has obvious roots in the wattle fences of Medieval England. The riggle rod fence was the most effective in creating a barrier to keep things in or out of an enclosure. This fence type was constructed using three horizontal longers with long slender branches woven alternately between the longers creating an over-and-under effect. The tops of the branches were usually left untrimmed at the top. The branches were pushed close together and once they dried, the fence formed a very strong barrier. This type of fence was economically practical because it did not require the use of nails
on the woven uprights."
While this seems to be an east-coast tool to keep out wind and wildlife, I think it will suit our yard and gardens perfectly. It not only allows me to build it as I can, but also allows me to build it cheaply with saplings from the surrounding forest. Natural, useful and inexpensive ... what more could a gardener want?