Balancing Fairness and Justice: When Just Right isn't Enough

As an arbitrator (or a Judge) we have limits--on our outward demonstration of compassion, our creativity in crafting appropriate and fair remedies and our moral indignancy where wrongs occur without remedies.  As poorly as we may feel about how someone was mis-treated, we are constrained to follow the letter of the law (even where it may be at odds with it's "spirit") and dole out remedies only where each element of a given cause of action has been proven by a preponderance of evidence together with actual, credible, available damages.  Yet, life is messy.  Memories fade.  Documentation is not always what we wish it were and hindsight is not always perfect.  At trial, the evidence may not be sufficient to meet those high standards.
This week I was challenged by a multi-day arbitration where I felt personally torn between the dictates of "justice" (technically, the respondent had no legal obligation to keep an unwanted, at-will employee when a new Supervisor came in who disliked him) and the cry for "fairness" which may have dictated he be given some notice, explanation, that the termination be based upon legitimate "cause" or at least that he be given some recognition for the many years of service that the employee had given prior to the termination.
My struggle ended with my own suggestion to the parties that before they finish putting on all of their evidence (and possibly becoming further emboldened in their positions) and before I was forced to apply the law and reach a verdict which would be adverse to one and victorious to the other, perhaps they would like to engage in settlement discussions.  Five hours later, and to my great relief and their great surprise, they had arrived at a very creative and fair settlement--which had less to do with "justice" than my verdict would have, but everything to do with "fairness".  I am confident that 2 days into trial, had I not suggested this approach, the parties would not have recommended settlement discussions to their respective clients.  Both had engaged very competent counsel to win.
Sometimes, a neutral third party is exactly what the parties need to arrive at the delicate balance between "fairness" and "justice" that we try to maintain.  Do other arbitrators dare to recommend settlement discussions during the evidentiary hearing?  (I did not serve as the mediator, by the way, because no one was expecting this would work--so they wanted me to continue the hearing if it failed.)
I offer this experience as hope for a more balanced future outcome on the tough ones!