I think you're thinking of the Munton's tabs. They are smaller. 3 Coopers tabs in 12oz would likely result in very over carbonated beer or bombs. The directions on the Coopers tabs say 1 per 12oz or 2 for their "large" (700ml?) PET bottles. I've never had a problem using just 1 in 12oz. You might be able to use 2 in 12oz, but it'd be pretty fizzy.
Suthern-I had this crazy vision of me with a tiny hacksaw, at the counter trying to cut these puppies in half.
Must need more drink...
As far as them not dissolving, I recommend flipping your bottle over once after a day. It seems to help mine dissolve better. I had a few of the large PET bottles that the tabs just wouldn't dissolve. I think they got stuck to the bottom and yeast flocculated over them, preventing the beer from touching them.
Terje