In my opinion, this is the true value you get from negotiation; just as useful as the extra salary itself. If you end up winning the negotiation but you see resentment and a lack of respect in the process, it should give you some information about the kind of party that you are dealing with. Additionally, it should mean you can get all of your offers up to the max reasonable range you'd expect, and then you have the option of going with the one that feels the best, where you're most convinced you'll be working with good people.
That's the critical part. You want to max your salary but not compromise integrity in the process -- if you make another 2% in first year salary but you end paying much more in sanity, poor fit, burnout, or lack of growth opportunities, you won't end out ahead. Get what you're worth in the short term, but be greediest about the long-term.