Should I appeal my paper's rejection in PRL? My manuscript in PRL was rejected after two rounds, although apparently quite narrowly. 

First round the paper was sent to two referees. One was very supportive to accept, and the other provisionally rejected but was willing to see what we had to say in response. 

Second round we actually got both of the original referees to accept the paper. But for whatever reason the editor sent it to a third referee, who recommended to reject the paper. Typically PRL ends the review process at two rounds: it always rejects if there is no complete consensus to accept the paper after two rounds. 

We agreed among us that the argument is not a deal killer, definitely fightable if we have the stomach for it. 

As far as I can see we have a few options, and am wondering which we should go for.


Ask for a further round of review. Although the review process is technically over, in our collective experience, the editors will typically oblige your request, and even more so when you've got two good acceptances. The downside is that you have no idea how many additional referees you will end up having to fight with - some of our friends have ended up with 5 or 6 referees, not the easiest considering how PRL referees are like. 
Appeal straight to the divisional associate editor, the default course of action. What this person says is final, even if it's to overturn two acceptances. 
One of the lower Physical Review journals has offered to publish as a 'rapid communication' without further review. 


Any advice?
Remember that editors often have to reject papers even if all reviews are positive. The reviewers only see the paper at hand, the editor sees all papers submitted, and all papers with only positive reviews are often still way too many to be all accepted. So by necessity, the editor also needs to reject papers with all positive reviews. Passing the hurdle of getting all positive reviews is often a necessary but not sufficient condition to be published, your paper also need to be better than a large portion of other papers that also passed that hurdle.

Bottom line: fighting editor decisions is usually not worth it, especially if you have another accept ready.