Late Sunday, Amazon unveiled an unusual deal: Starting this week, the online retail giant can get your packages to you on Sundays, and the delivery truck will say USPS, not FedEx or UPS. That's right: The U.S. Postal Service, which was all but begging to stop Saturday mail service — until Congress shot down the plan — is now working Sundays.

At first glance, this sounds great. Amazon isn't charging any more for Sunday delivery, so if you're an Amazon Prime member, for example, you can order something on Friday and have it arrive Sunday free of charge. Even if you're not a Prime member, those five to eight days you'll wait for your bargain-delivery order now include the (Christian) sabbath.

However, there are a few caveats — e.g., not every item will be available for Sunday delivery. There's also one very big catch: You probably won't benefit from the new deal, at least not this holiday season. Or maybe ever. That's because USPS is only delivering in two markets at first: the New York City area and metropolitan Los Angeles. That encompasses a lot of people, but only a small fraction of the U.S. population.

Amazon and USPS plan to roll out Sunday package delivery to other large metro areas in 2014 — Dallas, Houston, New Orleans, and Phoenix, among them. That will cover, as Amazon says, "a large portion of the U.S. population," but if you don't live in or right outside a major city, don't hold your breath for Sunday delivery. And keep in mind, you can already get almost anything you might want in New York and L.A. on Sundays, or just about anytime.

Still, the option of Sunday delivery is nice for New Yorkers and Angelenos. It's also being called a win-win for USPS and Amazon. The Seattle online superstore gets something no rival has, large-scale Sunday delivery, and thus creates another compelling reason to shop at Amazon — or even join Amazon Prime.

"Delivery on a Sunday would be very compelling for consumers," Forrester Research analyst Sucharita Mulpuru tells The Wall Street Journal. "There are certainly people who decide not to make an order on a Friday because it won't get there until Monday."

For its part, the USPS gets some much-needed cash. The postal service expects to lose about $6 billion this year, if Congress allows it to raise stamp prices, and that's still an improvement from last fiscal year's $15.9 billion loss. That's not all the USPS's fault: Congress not only won't let it cancel Saturday mail service, but starting in 2006 it also forced USPS to pay about $5.5 billion a year into a retiree health fund — the only government agency that has to do so.

As first-class mail volume continues its precipitous drop, packages are becoming a financial lifeline for the post office. Even when it wanted to drop Saturday mail service, the USPS never proposed ending weekend package delivery.

USPS actually already delivers packages on Sundays, albeit on a very small scale. Now it will have a virtual monopoly, since UPS doesn't deliver on Sundays and FedEx does only rarely, for an extra fee. Amazon says it chose USPS because their technology and infrastructures work well together and because, as USA Today notes, "the USPS is the only delivery service that reaches every address in the nation — 152 million homes, businesses, and post office boxes."

But delivering to every U.S. address isn't as much a competitive advantage as it is a congressional mandate. The decision to roll out Sunday service in just New York and L.A. may be party because that's where Amazon has the infrastructure in place, but keeping delivery constrained to high-density areas will also be profitable for the USPS, which should use less fuel and fewer employee hours to deliver more packages for greater profit.

In fact, USPS says it won't even have to hire anyone for the new service. The post office has been working for more than a year to cultivate a "flexible" workforce willing to work Sundays, says USPS spokeswoman Sue Brennan. "We're ready for Sunday in the current markets," she tells The Wall Street Journal. "If this were to expand, we would look at staffing levels and adjust accordingly."

The USPS will expand Sunday delivery if this limited venture proves profitable enough, if Amazon keeps paying for breaking the Sunday barrier, or if other companies start contracting the postal services' Sunday option. "As online shopping continues to increase, the Postal Service is very happy to offer shippers like Amazon the option of having packages delivered on Sunday," says Postmaster General Patrick Donahoe.

Note that the happy offer is to shippers, not customers.

And that's kind of the bottom line: The USPS needs money, Congress is tying its hands, and this is one deal where the mail carrier doesn't have to waste money driving hours down a dirt road to deliver a single package. Snow, rain, heat, and "gloom of night" won't stop you from getting your Amazon package on Sunday, but economies of scale just might thwart you.