While computers have changed drastically over the past 20 years, morphing from big boxes to svelte laptops, touch-screen tablets, and smartphones, the Web browsers we use on them have looked largely the same.

Sure, you can take a desktop Web browser, optimize it for a smaller screen, and add some touch features—as the most commonly used mobile browsers do. But the results are often inelegant, because the things you do online on a laptop or desktop computer tend to be different from the things you do on a tablet or a smartphone. And chances are you’re not using a traditional keyboard and mouse, the tools that desktop browser makers could count on you to have.

Opera, the largest of the small-share browser makers, recognizes this with the recent release of its free Coast browser app for the iPad. Coast represents a major change in the look and feel of a tablet Web browser. It’s the latest in a long line of browsers that have tried new approaches (see “The Browser Wars Go Mobile”), but it may be the first that really makes it work.

As the name implies, Coast is more for sitting back and watching where the Web takes you—truly browsing—than for going to predetermined destinations. The app banishes the standard URL address bar, treating your favorite websites as on-screen tiles and hiding most options. While it could use a bit more polishing, it’s a clever reimagining of how we can experience the Web on a small touch screen.

Coast first surfaced this year in a leaked video showing an early internal presentation of the browser, which Huib Kleinhout, an engineer at Oslo, Norway–based Opera, started as a side project a year and a half ago. In an interview, Kleinhout told me he wanted to simply build a browser “for the Internet of now,” in which websites are more complicated than ever and there are orders of magnitude more pages than there are apps in any app store.

Coast takes cues from apps and mobile operating software to do this: favorite websites appear as a bank of brightly colored square tiles against a dark background, up to nine of them on each virtual screen. That’s plenty if, like me, you visit only a handful of websites regularly.

Tapping a tile for, say, Reddit opens a screen-filling page with no borders or URL bar at the top. Swiping down on the page refreshes the content. Tapping a tiny cluster of nine white squares at the bottom center of the display takes you back to the home screen, while hitting a line of three little white squares on the bottom right allows you to scroll sideways through all tabs you have open.

Viewing the Web this way—without tabs and options constantly in your face—forces you to relax. I found I was more inclined to click around within websites, reading more content on different pages, rather than flitting from one site to the next.

If you want to search for a specific term or site, start typing it into the search bar on Coast’s home screen. The app will offer autocomplete suggestions via Google or let you search for your term on Google itself, and it will present a handful of clickable tiles for websites it thinks you may want to visit (tap the word “new,” for example, and you might get tiles for the online electronics retailer Newegg and a couple of news websites).

One sweet feature is the absence of back or forward buttons. Instead, you swipe to the right or left. Smart, right? I also liked how page-sharing features are hidden under an icon on the bottom right of the screen.

It’s a first public version, though, so understandably Coast could use some work. Its city-at-night background and script-like logo feel dated. Pages sometimes froze, and several times the videos I watched through the app were glitchy. Coast failed to detect my intention to open links on several pages.

Still, Coast represents a fresh, enjoyable way to think about browsing on a tablet, with minimal distractions so you can sit back and relax.