Hi Arty and Mike,
I will check out the Ashton link you posted Mike Matrix, and re: "Vestibular Exercises," Arty. I hope you don't mind me adding to this thread that I have found that continuing to do yoga during tolerance has helped me with my balance and strength very much and I will continue doing it through taper and complete w/d. There are some good "core" postures that can really strengthen balance, and you can find hundreds of links on line for yoga postures, many of them with free instructions, info, photos, and so on.
Standing on one leg, with the other knee bent out to the side and the bottom of the foot held against the ankle, calf or knee is similar to what you described standing on one leg, (alternating sides) and that helps with further balance, and is known as the "Tree Pose" in yoga.
Here's to us all being strong to the core like hearty oak trees.
Best regards and good wishes,
Also, here is a link I found on Vestibular Exercises that looks comprehensive:http://drnguyen.ucsd.edu/Default.aspx?tabid=77