I believe in enjoying happiness and not worrying whether other people think you've been given enough of it. Who cares what others say about "one round of salary negotiations"? If you're happy with the offer, accept it and thank the company.
Some companies make their offer, and that's it -- they won't budge. This company might be willing to negotiate, but you must consider what happens if they don't. If they balk at the extra two grand, then you're going to look weak coming back and saying, "Well, okay, then I'll take what you offered anyway." It says something about your request: you couldn't justify it. And what does that say about your credibility? Remember: you're going to work with these people. How you handle negotiations can affect how they will view you -- and treat you -- once you're on board.
If the extra money really means a lot to you, then go for it. Here's an example of how I might approach it:
"Thanks for your offer. I'm ready to accept it, but I'd like to discuss the salary first. In looking at the value of my skills in our industry, I believe I'm worth $2,000 more than you're offering. But I don't want you to misunderstand: This is not a large difference, and I have already decided I want this job. To show you my good faith, I'll accept your offer as is. But I'd like to respectfully ask you to consider raising it by $2,000. There are three reasons why I believe I'm worth it... But either way, I'm ready to start work in two weeks."
It's your judgment call. If you try this, you'd better be ready to prove your added value. By making a commitment to the company first, you establish a level of credibility that goes beyond any negotiating position.
Remember that the ultimate goal of negotiating a job is not to get every last dollar you can. It's to set the groundwork for the best possible work relationship -- which is not limited to money -- for the long term
. That's why it might be better to accept an offer that you're clearly pretty happy with, and plan for how you could get that extra couple thousand as part of your first raise when you have your first review