One of the major skills that a project manager has to develop is that of conflict resolution.  Since the work of projects is performed by humans, conflict is inevitable.  Rather than suppress the conflict, a manager might choose to embrace the conflict and turn it into a learning situation.

The highest form of conflict resolution is collaboration.  This is generally where the parties explore alternatives and try to make the "pie" bigger before slicing it up.  That being said, a manager should be aware that the other forms of conflict resolution (smoothing, forcing, withdrawing, and compromise) are all legitimate tools to use during the process.  Each tool has its place.  However, most of us have a default approach to conflict resolution and rarely tap the power of alternate approaches.

One thing to remember about compromise is that while you get to agreement, often both parties have given something up to get to that agreement.  If you can preserve the relationship and avoid hurting feelings along the way, a compromise may be a legitimate way to solve a problem.

If you read the Tao, you will find that the sages use smoothing and withdrawing as their primary approaches to conflict resolution.  However, no matter what approach you take to get to an agreement, Verse 79* contains much wisdom.

"After settling a great dispute
     some resentment is sure to remain
Being content with what you have
     is always best in the end

The Sage always assumes the debt
     as if holding the left side of the contract
He gives and gives, and wants nothing in return

One with true virtue
     always seeks a way to give
One who lacks true virtue
     always seeks a way to get
To the giver comes the fullness of life
     to the taker just an empty hand

Though the Tao of Heaven has no favorites
     it always sides with one who has a pure heart

*Tao Te Ching, The Definitive Edition, Lao Tzu with Translation and Commentary by Jonathan Star, Jeremy P Tarcher/Penguin, 2001, page 92