So, my main character, a berserker, has 20 constitution. I have noticed some fairly weird things with the regeneration you (should) get with that score. The most astonishing just now.
I loaded my save game, where all of my characters were at low hit points after a series of battles. But, lo and behold, the berserker had gone from about 40 hit points all the way to 135, just like that. Just from loading the saved game. This was so weird that I checked it again: when I load the screen where I can choose from among my save games, the icons clearly show that everybody is at low hit points. But when I load that saved game, my regenerating character immediately gains all his hit points back.