At 11 o’clock on a Tuesday night, Amanda, a senior at Princeton University, got her first text message from Stephen, a 60-something Wall Street banker. He wanted her at his New York City apartment. Immediately.

“I told him it was too late—the trains just stopped running,” Amanda said. “He said he’d send a limo.”

Amanda agreed, on the condition that she’d be back on campus for her 10 o’clock class the next morning. After dinner at a fancy restaurant, sex, and some post-sex apartment decorating, Amanda was back in the limo. When she got back to Princeton, she had just enough time to change her clothes, grab her books, and run to class.

Stephen is just one of the many men Amanda has met on Seeking Arrangement, a website that connects “sugar babies”—young, pretty women—with “sugar daddies”—usually rich, older men. On Seeking Arrangement, the most important part of the profile is the number at the top of the page: net worth. Men with annual incomes of over $5 or $10 million get the most attention. The site advertises “mutually beneficial relationships,” in which young women shower men with attention in exchange for “the finer things in life”—fancy dinners, extravagant vacations, or monthly allowances. What the site doesn’t talk about is sex. But sex, I was told by multiple sugar babies, is what everybody’s thinking about.

“’Sugar babies are escorts,” said Tammy Castle, a professor at James Madison University whose research includes analyzing the content of escort websites. “[The administrators of the Seeking Arrangement] are trying to avoid the negative stigma of prostitution by advertising this as just another dating website, but money is exchanged for arrangements that may include sex.”

In 2013, Seeking Arrangement announced that approximately 44 percent of its 2.3 million “babies” are in college. This is a trend that the website encourages—if babies register with a .edu email account, they receive a free premium membership (something the guys have to shell out as much as $1,200 for). Seeking Arrangement creates the illusion that the sexual element of these relationships isn’t forced, but organic. No one associated with the website wants to admit that what it’s doing is facilitating sex-for-money exchanges. The large number of college women on the site helps preserve this illusion, for both the daddies and the babies.

“Dating a college woman fulfills these guys’ wildest dreams. They want someone highly educated who is eager to learn,” said Parinda Wanitwat, director of the documentary Daddies Date Babies, which profiles several college sugar babies living in New York City.

In almost every message Amanda receives on Seeking Arrangement, sugar daddies comment on how intelligent she sounds in her profile. Amanda has met more than 50 men through the site. All of them are well-educated, the majority are business executives.

When she first signed up for Seeking Arrangement, Sarah, another sugar baby who recently graduated from college, was surprised by how many men sent her messages. Sarah has a curvy figure and is originally from Southeast Asia.  She expected the men to be interested in girls who were skinny, blonde, and white—“sorority Barbies.” “That’s just not me,” she said.

And yet, Sarah got a lot of attention on Seeking Arrangement. So did Sophie, a 27-year-old graduate student in New York City. She describes herself as an intellectual with pretentious glasses and curly brown hair.

“I look like what I am, and the men like that,” Sophie said. “They want someone who doesn’t look like a bimbo.”

On Seeking Arrangement, intellect is important—maybe even more important than looks. If the sugar baby can understand what the “daddy” does at work and engage in topics he finds interesting, he is more likely to feel he’s in a real relationship. “The guys eventually want to feel like, ‘That girl likes me for me,’” Amanda said.

While some men on the site use it exclusively for sex, the majority want sex and something else. They want someone to come along on business trips, go to company events, and meet their friends—someone who understands and appears interested in what they have to say. Most importantly, they want someone who will help them pretend that the relationship is not a transaction. Only one sugar baby I interviewed said she discussed her fee upfront, on the first date. The rest said they preferred to let the issue of compensation “come up naturally.”

The women I talked to found that avoiding a conversation about money actually led to more of it. When she first signed up on the site, Rebecca, a sophomore at NYU, asked potential sugar daddies about money right away—sometimes even before the first date. After a few months of making far less than her friends on the site, she decided to stop asking. She started waiting for the daddy to bring up the money issue and was immediately more successful.

Like Rebecca, Amanda never directly asks for money. Instead, she waits until the sugar daddy is comfortable enough to give her a credit card in his name.

“I get to a point in these relationships when the guy starts to naturally want to pay for things for me. They prefer giving me a credit card because it feels more informal. There is no direct exchange of money,” Amanda said.

In this way, it’s easier for the men—and, to a certain extent, the women—to pretend the transaction never actually happened.

“I found that some, if not most, of the guys don’t want to talk about money. I suspect that’s because it kills the fantasy,” said Wanitwat. “They’re trying to pretend that these smart, beautiful women actually want to hang out with them.”

The illusion works the other way, as well. When a friend of mine started to think about joining Seeking Arrangement in our senior year, she told me the site was extremely popular among college students. She said tons of girls at Columbia and NYU had profiles to help pay tuition bills. This made the website seem safer, and less like prostitution. If half the women on the site really were college students—and the guys had a particular interest in meeting college students—maybe the work wasn’t just purely physical. Maybe it really was about the conversation and companionship, not just the sex.

When we consider what it means to be a high-end prostitute, we generally think about Julia Roberts in Pretty Woman—a desperate young person willing to trade some of her dignity for the chance to avoid working on curbs at two in the morning. A college education seems fundamentally at odds with that image. By actively seeking out college students, and publicizing the high numbers already in its ranks, Seeking Arrangement makes it easier for smart, young women with bright futures to rationalize the decision to join Seeking Arrangement: If so many college women are signing up for the site, it must be something different. It must be more socially acceptable somehow. It can’t really be prostitution.