It wasn't too long ago that I stood in your shoes.
I summered at a firm in NYC and shortly after receiving the offer, the firm was no more. Offer kaput.
I'll get back to that in a minute.
Most lawyers wind up in their practice by means other than choice. If International blah blah is your choice, you may have limited choices as a 3L. So explore other options. Money may have to wait.
After my firm job collapsed, I looked at gov't, etc., and ended up as an ADA in NYC. Great job, shitty pay. But I ended doing something I love. Trial work is one hundred thousand times better than document review. From there I went federal, and the rest is history.
Point is, headhunters have their best interests in mind, and that doesn't mesh with a law students interests. They look to fill specific needs, like a sixth year with heavy '33 act experience. They have little use for you. If international commerce is your thing, try and find a smaller firm, or government agency that will give you REAL experience. If money is all you desire, take whatever you can get in BigLaw. But don't expect a headhunter to get you there.