Who are the counterparties?

I read this morning in the WSJ that the price of insuring a portfolio of Greek sovereign bonds has risen dramatically in recent weeks. This is natural, and unsurprising in itself; however, it reminds me to ask, Who are the counterparties to these insurance policies? I don't know the answer, but it seems important.

In my mind, of course, is the collapse after the Lehman default of AIG, brought about by the its CDS obligations.

Here's a metaphor for the AIG collapse. A bunch of delinquent financiers decide that selling insurance against the failure of the sun to rise would be good business. I mean, it's not going to happen! ("And even if it does, the buyers won't be able to find us in the dark", they must have thought.) Unfortunately, there were no buyers for this instrument. Why? Because it's not going to happen. So they decided to sell insurance against something that might happen, but probably won't. Unfortunately, the "it's not going to happen" part of the plan was the crucial element that made "sun insurance" a good idea. The AIG losers didn't plan for the Lehman default scenario any better than they would have prepared for the failure of the sun.

Now, I (half?) expect that the community of high finance practitioners has noticed the difficulty, and worked it out this time. That is, that someone has taken steps to verify that counterparties to these CDS things will have sufficient capital to service obligations should Greece default. But even so, I still want to know how! Is there no such thing as systemic risk anymore? Have the financial engineers worked out sun insurance, too?