The last offer I successfully negotiated went like this:

Recruiter: What kind of number are you looking for?

Me: I'm looking for a minumum of $num. (A 25% raise from current gig)

Recruiter: We can totally do $num.

<a week or so passes while they put the offer together>

Recruiter: We're offering you $num.

Me: Could you do $num + ($num * 7%)?

Recruiter: I'll see what I can do.

<a week or so passes while he gets approval>

Recruiter: We're offering you $num + ($num * 7%).

Me: Sounds good.

Now, a professional negotiator probably wouldn't have coughed up a number first, but my gig at the time was paid fairly and I really liked the company. So I tossed out a number that was big enough to actually get me to jump ship. Was no skin off my back if they couldn't reach it. But they could. And I had a pretty good feeling from the hiring manager that they wanted me there, and that they'd advocate for me with HR, which I'm pretty sure is what happened.