Recently, I read about peace renegotiations to get techs (and other things) cheaper (in the Strategies & Tips forum. Aren't you glad I'm a Civ3 Forum Moderator?
). Now, if I read this correctly... then it's an O'Glorious Loophole. 
The demogame constitutition states:
It seems we CAN renegotiate peace, even when we're not in a war, to see what's on the bargaining table. I'm not sure how this affects current treaties (I did a test in some of my own games, and they seem to stay), But, you "politely extort" civs while making them happier. (I guess they know they won't be annihilated in 20 turns.
) It's best if you do it when you first meet a civ (Important note for our next demogame!), but you can renegotiate at any time.
Here's an example:
I started a new game as Japan. (The screenshots are self explanitory)
Before
After
I'm not sure if we can renegotiate to check for trades just like normal trades, but I think that's what the constitution is saying... (I could be wrong, though)


The demogame constitutition states:
- It is unlawful to play through actions, move troops, make deals or take any other action that would change the state of the playing game from that of the saved game.
- Exception: The structure of --> peace renegotiation treaties <-- requires an action to be taken to view the bargaining possibilities. Specifically, once the deal is broached it must result in a new deal or a declaration of war. Once the bargaining possibilities have been noted the altered game must be immediately closed without saving. Further activity in the altered game is not allowed.
It seems we CAN renegotiate peace, even when we're not in a war, to see what's on the bargaining table. I'm not sure how this affects current treaties (I did a test in some of my own games, and they seem to stay), But, you "politely extort" civs while making them happier. (I guess they know they won't be annihilated in 20 turns.

Here's an example:
I started a new game as Japan. (The screenshots are self explanitory)
Before

After

I'm not sure if we can renegotiate to check for trades just like normal trades, but I think that's what the constitution is saying... (I could be wrong, though)