your power definitly increases your diplomatic power... theyll accept even offers that are bad for them. Ive been bogged down many times... i once had 6 full stacks wandering round my capitol... i blocked the bosphorus so they laid siege to nicaea... i defeated them after a few turns and they came begging me for a ceasefire, you can really ask them a lot of money than :P... so one or 2 major victories will usually give you a good peace for which theyll pay you a good load of money when you do it good