(FORTUNE Small Business) – It is natural to root for the Ceci brothers, who own a landscape contracting business and recently emerged victorious after an eight-year court battle against jillionairess Leona Helmsley. On the surface their victory--they were awarded $117,000--would seem an inspiration to every small-business owner struggling with a customer who can afford to pay but won't. However, under the neatly mulched surface lies a rich load of mud and manure.

Helmsley, a New York City hotel hotshot, owed the Ceci brothers about $53,000 in October 1995 when, without explanation, she instructed her guards to deny Ceci employees access to her 26-acre estate in Greenwich, Conn. Some of their lawn mowers and rakes stayed trapped inside. This crisis erupted in the seventh season of her relationship with the firm, which collects annual revenues of more than $10 million. Though Helmsley had been branded the Queen of Mean the galaxy over for her harsh treatment of workers, she had been a "nice account to land," recalls Michael Ceci, 39--whose definition of "nice" translates into $200,000 in annual billings. "We had a very healthy relationship with her," adds Robert Cardini, 38, the company's operations manager and a brother-in-law working with the four Ceci brothers. "She paid all her bills."

Until one day she stopped. Technically the money Helmsley withheld from the Cecis was for garden-variety maintenance. But relations between the two parties slid downhill following a separate assignment that the brothers had taken on for her earlier in 1995: constructing a 15-foot-tall, 300-foot-long hill.

Helmsley wanted the hill to obstruct her view of the construction underway next door. Her idea of next door was "so far you would have to use binoculars to see it," says Michael Ceci. After two months of extensive earthmoving, word came down from the unfinished mountain--the 45-foot Norway spruces weren't even in yet--that Helmsley had changed her mind and wanted her original lawn back. "We were stunned, but we said, 'Okay, if that's what you want, we'll do it,' " says Michael. So how did they end up getting locked out soon after? "The poor Ceci brothers just did exactly what they were told," insists Andrew Nemiroff, their attorney. Their mistake: thinking that was enough.

This fracas could be a case study for a college course in Marketing to the Rich and Fickle. In today's economy, selling a service--hill building, say--isn't merely about moving dirt efficiently at the lowest price. More than ever, successful marketing requires forging a bond with the customer. The Ceci brothers "should never have let her believe that this was just another mountain," says Bruce Weinberg, an associate professor of marketing at Bentley College in Waltham, Mass. "They should have helped her see that this was her special hillside."

A month before the bust-up, Michael Ceci and his young son, Ben, gave Helmsley a tour of the area in a golf cart. By all indications, the outing went fine; Helmsley even sent the toddler a stuffed bear. But in retrospect, might Ceci have made a more memorable connection by transporting her via horse-drawn carriage--and laying out a cozy picnic lunch? Helmsley wasn't just buying a mound of soil, she was investing in her privacy. She needed to touch the mountain, lie down on it, maybe even roll around where no one could see her. Imagine her galloping back clasping a vial of virgin soil, keeping it near so that she could feel close to her mountain. Never mind that ultimately "her view was that it was a monstrosity, and she didn't like it," says Leonard Fasano, Helmsley's New Haven-based attorney. Would she have felt different if it had cost her more than the $200,000 she spent? A tycoon like Leona hears rumors of a peer's spending $500,000 on a new mound and wonders whether she's getting something second rate. The Ceci brothers won the case, but they shouldn't neglect the lesson: Treat each of your billionaire clients as someone special.