There is a lot of fiction about how to negotiate settlements of government contract claims. In reality, there are a few principles which are immutable, unassailable and nearly universal in application. Here are my favorite few.
Bargaining position. Know your bargaining position and enhance it. Don't enhance it by bluffing (see below). Know the opposing party's strengths and weaknesses and be equally circumspect about your own. Get outside help. Listen to others about the relative positions. Set a realistic goal based on your position. Don't negotiate if your position is demonstrably weaker than that of the other side.
Preparation. Prepare, prepare, prepare. Hire experts to help. You can significantly increase your bargaining position by intensive preparation. Exhaust this one. The side that is the best prepared will always come out with a good result. To win the battle of the experts, document, document, document. Rehearse, do mock negotiations and hire a mediator to critique your approach.
Bluffing. Don't. Two problems. You probably are lying and the other side most likely will think so. And, the other side may well call your bluff or completely ignore it as if you have not made it. Taking an extreme position is nonsense. A reasonable person on the other side will just ignore you. You must have integrity and nothing kills that like bluffing.
Splitting the difference. This is time honored. But there is a time and a place for it. Always split the difference when the positions are close. Never even think about it when the positions are far apart. This is always the last resort. Offering to split the difference must be made when the negotiations have been exhausted.
Honesty and sincerity. At the foundation of the real art of the deal is a negotiator who has a reputation for honest and sincerity. You have to be believable. The other side must know that you tell the truth and that you are candid and forthcoming. This also means you are not given to game playing and tricks commonly associated with used car salesmen.
In the end, success may well include other factors. But you are unlikely to succeed without following these five fundamental principles.