A good manager doesn't try to eliminate conflict; he tries to keep it from wasting the energies of his people. If you're the boss and your people fight you openly when they think that you are wrong -- that's healthy.
If you don't do it with excellence, don't do it at all! Because if it's not excellent, it won't be profitable or fun, and if you're not in business for fun or profit, what the hell are you doing there?
Compromise is usually bad. It should be a last resort. If two departments or divisions have a problem they can't solve and it comes up to you, listen to both sides and then pick one or the other. This places solid accountability on the winner to make it work. Condition your people to avoid compromise.
Most managements complain about the lack of able people and go outside to fill key positions. Nonsense. Nobody inside an organization ever looked ready to move into a bigger job. I use the rule of 50 percent. Try to find somebody inside the company with a record of success (in any area) and with an appetite for the job. If he looks like 50 per cent of what you need, give him the job. In six months he'll have grown the other 50 per cent and everybody will be satisfied.