PayPal is making some of the advances it’s pushed in mobile-app payments available on the Web, the company announced Tuesday. Its in-app checkout experience, which it calls One Touch, is now rolling out to websites which already use PayPal’s payment technology.

Consumers will notice a new option to stay logged into PayPal, which will remember their payment options. In a marked change, PayPal will no longer force shoppers to change their payment method from a default bank-account withdrawal; instead, the service will remember the credit or debit card or bank account they prefer, and use that each time. It’s how PayPal works in mobile apps already.

Bank-account withdrawals are more profitable for PayPal, as I noted when I interviewed David Marcus, then PayPal’s president, in January 2014. “That’s over,” Marcus told me, vowing to change the checkout experience to be more straightforward. Now that day has come: PayPal is no longer tricking its customers into using a payment method they may not prefer.

PayPal checkout now remembers your payment preferences and shipping address, saving you clicks and typing.

Mobile First—And Then The Web Must Follow

There’s a deeper significance to PayPal’s move, one the whole industry should pay attention to. It’s an example of a technology first designed for mobile devices that is migrating into the broader Web. Consider how Flipboard, a company which became famous as an app developer, is now shifting its news-reading experience back to the Web.

For years, the innovation in e-commerce has been focused on mobile apps. That’s where PayPal’s Braintree subsidiary made its name, powering frictionless mobile transactions in apps like Uber, Airbnb, and HotelTonight.

That click-and-you’ve-paid convenience has been missing from the Web, which still uses a confusing array of popups and redirects to process even simple e-commerce transactions. When you squeeze that Web shopping experience into a mobile browser, the result is disaster—or, to use the technical term, abandoned shopping carts.

Bill Ready, the former CEO of Braintree who was recently promoted to be PayPal’s global head of merchant and next-generation commerce, says that his customers were seeing a 50% rise in completed purchases by adopting the simpler One Touch checkout process within apps.

See also: PayPal’s Startup Guys Have Seized The Company’s Reins

“We saw such huge results that we’re taking the native buying experience and rolling it out across the Web,” says Ready.

Most sites using PayPal won’t have to do anything to get the upgrade—it will happen automatically through the code their sites call up from PayPal’s servers.

Ready notes that this upgrade will be easier on merchants than on mobile, where PayPal required developers to adopt a new software-development kit, the V.zero SDK.

He admits that PayPal hasn’t done extensive testing that lets it predict the kind of uplift that websites will see from a simplified checkout experience, but he predicts that particularly on mobile versions of e-commerce sites, online retailers will see more completed purchases.

Some Things Still Don’t Check Out

Ready’s team hasn’t quite finished the job, though. Even before PayPal bought Braintree, Ready was touting a vision of e-commerce where his company’s servers would safely store credit and debit cards and let consumers use them from site to site and app to app.

This latest upgrade to PayPal’s checkout doesn’t integrate with Braintree’s so-called “vault” technology. If a customer has stored a credit card with Uber, a Braintree merchant, in an app on her phone, she won’t automatically have that card available when she shops on her laptop for dresses at Jane.com and checks out with PayPal. (Nothing’s stopping her from storing the same card in both places, but eliminating that busywork of entering a card over and over again is what Ready’s vision is all about.)

PayPal president Dan Schulman, who’s slated to become the company’s CEO when the payments company spins off from eBay Inc. later this year, hinted that more change might be coming in a recent eBay earnings call—specifically touting Ready’s role in combining PayPal’s disparate systems, which include Venmo, a person-to-person payment system which serves as another kind of digital wallet for debit- and credit-card accounts:

Bill as you know was the CEO of Braintree, and what we really did by putting that together is … combine the Braintree platform and the PayPal platforms much more closely together so that we are able to being able things like One Touch not just on full-stack integrations and on mobile, but into the PayPal base … And so we are taking the things that we’ve learned through both Venmo and Braintree, putting them together with some of our other acquisitions to provide to our PayPal embedded base, not only the services that you see now, but services that we will introduce even as of this quarter that will take us to a whole different level as a result of that integration together.

There are a couple of months left in this quarter. Plenty of time for Ready’s team to lash together more of the company’s systems—all in the name of faster shopping.