If you have a Birkenstock shoe store near you, get a small bottle of "Cork Life" and it will do the job very nicely. It is only a couple of bucks and one small bottle lasts forever!

I'm curious about the "Cork Life" product - (I know that they used to sell some stuff that you would put on the edges of your Birks to keep them from crumbling - looked a lot like Elmer's glue to me.) Is Cork Life an oil?

Somewhere - possibly in Michael Sinclair's bamboo restoration book - I've seen the suggestion of using a dab of baby oil and I've been happy with that. It may come down to whether one prefers the smell of baby's bottoms or lemons.