A Means to an End
Very few people like to negotiate. It's a huge headache for everyone involved, and a successful negotiation is usually when both sides feel the other side got the better deal. This is not a very positive way to start out with a company.
If you can't get what you want by asking, negotiation is a necessary evil.
So that begs the question...
What Are You After?
You wanted to get this job with a good salary.
They went above any beyond what you asked for.
What will you gain by negotiating further? Just negotiating for the sake of negotiation may just be...
Grasping Defeat from the Jaws of Victory
You asked. The company delivered. No negotiation necessary. They are so happy with you that they gave you what you wanted to get you on board.
What will it say if you push for negotiation just for the sake of it?
- "I don't know when to quit while I'm ahead"
- "It's about the principle of the thing -- I am never satisfied"
- "I didn't really want the job and just wanted to use a good salary offer to dangle over other companies I am negotiating with"
Nobody likes moving goal posts (especially not hiring managers).
Speak Now, or Forever Hold Your Peace
That said, this is your last and best chance to set where you start from.
It would be nice to think that the company will correctly evaluate your salary next year and give you a bump if deserved, but many companies don't work that way. Salary increases are usually a percentage of your base salary, so a bigger salary with a similar percentage increase will mean compound growth on whatever gains you get from this negotiation.
At the same time, it may create some bad blood with the hiring folks at your new company, so who you're negotiating will have a big impact on how you should proceed. If you're going to be negotiating with your new boss, who has the power to determine your salary increases in the future, he may give you more now at the expense of raises later. That's something you will have to decide.
The Grass is Always Greener...
Humans are designed to regret losses more than they value gains, so the thought of not negotiating at all would feel like a loss that's hard to stomach.
At the same time, what makes us happy isn't money, it's a good work environment. If the money is good enough for you, it may be worthwhile to minimize the potential negativity that could come from a negotiation, and be happy with what you have.
Either way you decide to go, tell yourself that it's the right decision, and don't second-guess it. That will only cause gnashing of teeth in the future. No sense crying over spilt milk.