Hmm, possible downer on that scheme...
The departmental secretary's face when I mentioned Swisscare was not encouraging. Apparently, it can cause a lot of trouble and removes some of your rights as a patient. She said it's really not the best option and recommended (as we're young and not likely to keel over any time soon) getting a normal insurance with a large excess/franchise of about CHF2,000. For the three of us it works out as CHF390/month, which is about CHF150 more, but you're better covered.
I'm going to have to start printing cash at this rate...