By chance I made an interesting discovery.
This year I changed canton, so I let my health insurance company know my new address. They acknowledged it and sent me the new premium to be paid together with the new increased premium for 2012. In the old canton it was one of the cheapest premium, but in the new canton with the new premium they were about 30-40% percent more expensive than the cheapest alternative. So I give them notice saying I'll leave at the end of 2011. So far so good. As I didn't communicated the name of the new insurance company they sent me a letter saying that the cancellation is valid only if they get the name of the new insurance company. Here comes the interesting part: together with the letter I got payments slips for 2012 with a reduced amount. It would be no increase, moreover they would reduce the 2011 rate!!
I've already changed the insurance company and I don't intend to consider the new offer, because the new one is better. But anyway threatening to leave is something to be considered and may get you a rate reduction.