re: Best Way to Counter Offer

Are you just graduating or do you have work experience? If you are just graduating, then you probably don't have a leg to stand on. If some other company really did offer you more, but you want to work for this one, then tell them that. They may offer more. You just have to be prepared if they withdraw their offer altogether.

If you have more experience than what the qualifications for the position are, then I would think that it's expected that you negotiate a little bit. You might be better off asking for more benefits such as vacation, though.