As the founder and CEO of the Las Vegas-based software-development firm Gunner Technology, Cody Swann updates apps for his clients all the time. Occasionally, his employees have to take the apps offline to do this--after informing the clients, of course. But these alerts can get forgotten--and one time, after ignoring such a warning, a client got angry about being unable to access the software and threatened to fire Swann's firm.

Fortunately, Swann keeps receipts. He forwarded the client his initial email notice that the app would be unavailable, and saved the business: "I got a short reply telling me not to worry about it." How often does he face similar disputes, with customers who don't realize they're at fault? Swann laughs: "Almost every day."

There will always be customers who demand the impossible, misunderstand what you tell them, or blame your company for something that was out of your control. But figuring out how to keep these people satisfied is crucial to your business success. "It's incredibly tricky to determine the proper way to deal with a client who is wrong, but it is a necessary skill," says Nate Masterson, founder and CEO of Maple Holistics, a beauty-products company in Farmingdale, New Jersey.

So what should you do when your customer is wrong?

1. Stay calm.

Take the time to gather all the relevant facts, and listen carefully before you respond. And keep your ego out of it; your primary goal should be to resolve the dispute and make your customer happy, rather than to "win" the argument. (Also, think twice before communicating by text or email, where nuance can be lost and tensions can escalate quickly.)

2. Don't point fingers.

Sometimes resolving a disagreement is as simple as allowing the client to believe she is right while offering a solution everyone can live with. Another Gunner Tech­nology customer recently complained that the company had eliminated a link to add photos to her website. Nothing had changed; the client simply couldn't find it. So Swann decided to create a more intuitive way to find the link going forward. "I could've said, 'Look, you've just wasted five hours of my day,' " he says. "But I didn't point fingers, and basically said, 'Yeah, you were right. It was hidden. So I made it more visible for you.' "

3. Remember, you're the expert.

You're especially likely to face these sorts of customer complaints if your company specializes in more technical services, such as computer programming, architecture, or law, according to Laurie Richards, a business communications consultant: "The customer doesn't understand enough about the area of expertise to know all the alternatives." Assume your customer is acting in good faith and needs to be educated, not argued with. Do that effectively and you can "go from a situation where you could have conflict to one where you're actually establishing goodwill and turning a negative into a positive," Swann says.

4. Prove your worth.

"I sometimes work with clients who are in the wrong," says Maria Casey, the founder of startup consultancy MCA Partners, in Venice, California. One of her customers complained constantly and eventually left MCA--only to ask to return shortly thereafter. Casey decided to perform an audit of her work for the customer, complete with recommendations about how profits could be increased going forward. The result? Casey's recommendations helped improve her client company's year-over-year sales by 300 percent--and put an end to the griping. "The more upfront and strong I am in my stance, the more respect I end up getting," Casey says.

5. Know when to give up.

Some customers can't be satisfied. And some will always put the squeeze on those they work with, making baseless charges or unreasonable asks in an effort to cut the bill. How you choose to handle these situations comes down to how valuable you find the customer: "If a $1 million client balks at $1,000 in an invoice, you give in, no questions asked," Swann advises. "If a $10,000 client balks at a $1,000 invoice, you may want to give in the first time, but let them know you're doing so as a courtesy. If it happens again, walk away."