You may have noticed that the chair I sit on every time I go to the computer has no back. We took a look at this chair which is designed to keep your back very straight. You don't actually sit on your knees as it may look, most of the weight is on the seat and just enough on the knees to keep you from sliding forward. I use a chair like this all the time I work in my own office.
Then we took a trip to Backs Etc. in Toronto, a store that specializes in things to help your back, from the fanciest of chairs, to back supports and even ergonomic beds. One interesting comment from these experts: Don't simply try on a lot of different chairs. Decide exactly what you do in a chair (typing, talking, drawing) and tell that to the chair experts. Let them recommend a range of chairs that are best for your activities. I have friends who take their personal chair with them from job to job, and their productivity on and off the job reflects the usefulness of this practice.