Finding desirable tenants can sometimes be a pain in the ass too. But being willing to walk away is, of course, the best negotiating position.
Even when we lived in SF, where negotiations were almost impossible as they would have filled the unit within a week, they still were willing to do something in order to retain us.
think of the analogy "even money" in blackjack - when the dealer is showing an Ace but you've got blackjack, most objective people will take the "even money" versus gamble against whether the dealer has BJ or not. also why you tend to not split tens unless you're counting =p