For some businesses, great customer service simply means fast with a smile. For others—think luxury hotels, hair salons, and doctors' offices—it's all about time-consuming, personalized attention. The concern, of course, is that high levels of customer service can alienate those waiting in line and, eventually, depress sales. So how can customer service-intensive businesses strike a balance between quality service and high profits?

The answer: Limit the number of customers you serve, but charge them more, advises a recent study, "The Quality-Speed Conundrum: Trade-offs in Customer-Intensive Services." Scaling back on customers runs contrary to many entrepreneurs' instincts. But "for these businesses, there are no shortcuts around this need for individual attention," says Krishnan S. Anand, a business professor at the University of Utah and co-author of the paper, published in the academic journal Management Science.

The challenge is finding the ideal balance between service and speed, write Anand and his research partners, Senthil Veeraraghavan, professor of business at the University of Pennsylvania's Wharton School, and Fazil Paç, a Ph.D. student at Wharton. To that end, the authors have developed a set of mathematical formulas to construct what they call a queuing framework.

Here's how the framework might work: Say you run a spa or any other business that requires spending intensive periods of time with your customers. You spend 45 minutes on each client, charging $57 per client, and you would like to increase your revenue. The first step you might consider taking is shortening each session while keeping the price constant. The researchers' model, however, by using a series of algebraic equations that measure such factors as number of waiting customers, wait time per customer, and potential demand at varying prices, shows that you can maximize revenue by increasing each session to one hourand charging $85 a session.

As an example of a business successfully navigating the quality-speed tradeoff, the researchers point to concierge medicine, in which groups of doctors start practices that charge annual fees in exchange for seeing fewer patients and offering more personalized care. Although they focused largely on medical care providers, the authors believe their work is applicable to other businesses. "Customers don't want to wait while the person in front of them gets all the attention," Anand says. "But we all want the same attention."