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Here’s a little secret that Starbucks doesn’t want you to know: They will serve you a better, stronger cappuccino if you want one, and they will charge you less for it. Ask for it in any Starbucks and the barista will comply without batting an eye. The puzzle is to work out why.

The drink in question is the elusive “short cappuccino”—at 8 ounces, a third smaller than the smallest size on the official menu, the “tall,” and dwarfed by what Starbucks calls the “customer-preferred” size, the “Venti,” which weighs in at 20 ounces and more than 200 calories before you add the sugar.

The short cappuccino has the same amount of espresso as the 12-ounce tall, meaning a bolder coffee taste, and also a better one. The World Barista Championship rules, for example, define a traditional cappuccino as a “five- to six-ounce beverage.” This is also the size of cappuccino served by many continental cafés. Within reason, the shorter the cappuccino, the better.

The problem with large cappuccinos is that it’s impossible to make the fine-bubbled milk froth (“microfoam,” in the lingo) in large quantities, no matter how skilled the barista. A 20-ounce cappuccino is an oxymoron. Having sampled the short cappuccino in a number of Starbucks across the world, I can confirm that it is a better drink than the buckets of warm milk—topped with a veneer of froth—that the coffee chain advertises on its menus.

This secret cappuccino is cheaper, too—at my local Starbucks, $2.35 instead of $2.65. But why does this cheaper, better drink—along with its sisters, the short latte and the short coffee—languish unadvertised? The official line from Starbucks is that there is no room on the menu board, although this doesn’t explain why the short cappuccino is also unmentioned on the comprehensive Starbucks Web site, nor why the baristas will serve you in a whisper rather than the usual practice of singing your order to the heavens.

Economics has the answer: This is the Starbucks way of sidestepping a painful dilemma over how high to set prices. Price too low and the margins disappear; too high and the customers do. Any business that is able to charge one price to price-sensitive customers and a higher price to the rest will avoid some of that awkward trade-off.

It’s not hard to identify the price-blind customers in Starbucks. They’re the ones buying enough latte to bathe Cleopatra. The major costs of staff time, space in the queue, and packaging are similar for any size of drink. So, larger drinks carry a substantially higher markup, according to Brian McManus, an assistant professor at the Olin School of Business who has studied the coffee market.

The difficulty is that if some of your products are cheap, you may lose money from customers who would willingly have paid more. So, businesses try to discourage their more lavish customers from trading down by making their cheap products look or sound unattractive, or, in the case of Starbucks, making the cheap product invisible. The British supermarket Tesco has a “value” line of products with infamously ugly packaging, not because good designers are unavailable but because the supermarket wants to scare away customers who would willingly spend more. “The bottom end of any market tends to get distorted,” says McManus. “The more market power firms have, the less attractive they make the cheaper products.”

That observation is important. A firm in a perfectly competitive market would suffer if it sabotaged its cheapest products because rivals would jump at the opportunity to steal alienated customers. Starbucks, with its coffee supremacy, can afford this kind of price discrimination, thanks to loyal, or just plain lazy, customers.

The practice is hundreds of years old. The French economist Emile Dupuit wrote about the early days of the railways, when third-class carriages were built without roofs, even though roofs were cheap: “What the company is trying to do is prevent the passengers who can pay the second-class fare from traveling third class; it hits the poor, not because it wants to hurt them, but to frighten the rich.”

The modern equivalent is the airport departure lounge. Airports could create nicer spaces, but that would frustrate the ability of airlines to charge substantial premiums for club-class departure lounges.

Starbucks’ gambit is much simpler and more audacious: Offer the cheaper product but make sure that it is available only to those customers who face the uncertainty and embarrassment of having to request it specifically. Fortunately, the tactic is easily circumvented: If you’d like a better coffee for less, just ask.