Diagonal bracing would be best, and cross those legs. Cheapest around here would be 1/8" x 1" steel.
If you want it "guitar string" tight, drill your holes in the ends, lag one end on and heat a few feet cherry red with a torch (even a propane torch will help - do it during hot weather). Lag the other end while it's still hot. When it cools/shrinks, it'll be REALLY tight. Do that on all sides, and she won't wobble. Looks like a full stick (21 feet or so) would do each set of legs (cut each in half and cross). They would be about $10 each up here...
1x4 pine would accomplish the same thing...but not so tight, and much more visible.
Just my thoughts...course, I love steel. Can't stretch a board if you cut it too short, as Redlinger says.
