Convincing a stubborn client

So the client wants some unreasonable changes and you are definitely sure they are unsuitable if not entirely hair-brained. No one likes an argument especially with a client or even the project team leader. It strains the working relationship and at the end of the day even if you win the argument you still loose because you have a team member who may have still dug his heals and will probably stick to his beliefs only you wont know it until the next conflict!
So how do you go about bringing people around to share in your way forward in a project. Firstly dump the confrontational argumentative style. Go for persuasion. Persuasion is the art of opening up someones mind to something new not trying to convince them they are wrong. You can either go for their heart or their mind. The former means you have to be charismatic and lets face it not many of us are that persuasive so lets go for the mind. Here as an engineer or architect or even contractor our technical skills can come into play.
You will need to do your homework and come up with expert opinions and data to back your position. Also come up with significant benefits if things are done your way that benefit everyone. You have to be simple and rational, clear and logical so that the other person can clearly see the benefits.
Remember steer clear of proving the other person wrong otherwise egos may come into play and that would not be good for your plan. Also read the mood if the client is angry appealing to logic may not work as successfully unless emotions are allowed to settle