Tens of millions of Americans spend much or all of their days covered by Wi-Fi, and most smartphones can make voice calls over Wi-Fi. So doesn't it make sense for phone calls — through the main, default dialer — to be Wi-Fi-first, with the expensive cellular network used mainly as a backup, only when Wi-Fi isn’t available or strong enough? That’s the idea behind Republic Wireless, a small, pioneering phone carrier based in Raleigh, North Carolina, that I’ve been following since 2011.

Republic’s approach, which attracted press attention and a relatively small cadre of customers, allowed its plans to start as low as $5 a month and, in general, to be much cheaper than those of the big guys. Starting a few years ago, the company even figured out how to seamlessly hand off a voice call that began on Wi-Fi to the cellular network when the caller moved out of Wi-Fi range.

Still, there were limitations. Republic’s service worked with a very limited selection of Motorola handsets and only supported Sprint as a backup carrier. And it charged more than others upfront for the phones, which it had to specially modify.

Now, Republic has, in effect, broken out of jail. All of those issues have been solved. T-Mobile has been added as a second backup cellular carrier, and Republic’s service now works with seven top Android phones, including both versions of the Samsung Galaxy S7 and the latest Google Nexus models, whether you buy the phones from Republic or bring your own. If you buy the phones from Republic, prices are competitive upfront. The handsets need no modification and can even be switched to standard carriers if you don’t like Republic.

And its service plans, while no longer including a $5 all-Wi-Fi option, are still cheaper than those of major carriers, at least at the lower capacities.

Oh, and Republic has developed a new technology called "Bonded Calling" to improve the quality of Wi-Fi calls by filling in any gaps with cellular data, at no extra charge. The call, in effect, is running simultaneously over Wi-Fi and cellular data networks. Only when both fail to keep quality acceptable does the handover to cellular voice take place. It’s better for the customer, and cheaper for Republic than paying for more handoffs to Sprint or T-Mobile.

I’ve been testing this new Republic service on a Samsung Galaxy S7 Edge, the Korean giant’s $800 flagship smartphone. It’s equipped with a Republic SIM card and a Republic app, though Wi-Fi voice calls are placed through the main, default dialer.

To test the phone, I’ve made and received calls over my home Wi-Fi network, and commercial Wi-Fi networks at places like Starbucks. Every call went through, or was received, properly and clearly. When I walked down the block until I was out of Wi-Fi range, the calls handed over to the cell network without a hitch in every case. I even abruptly shut off Wi-Fi on the phone twice during a Wi-Fi call and the call continued on cellular without interruption (which kind of amazed me, even though I know the company keeps a backup cellular voice connection for each call ready in the cloud).

I also texted and performed data tasks, in and out of Wi-Fi, with no problem. Except for the tiny Republic Wireless icon in the corner of the screen and the network name, I’d never know I wasn’t on a standard network. You don’t even have to use the Republic app, unless you want to check your cellular data usage, or adjust settings, or change your plan — or even your phone number — right from the phone. If Wi-Fi is turned off or unavailable, a Republic phone will still make and receive calls over the cellular network.

So, what’s the downside? Well, Republic has dropped, for the new phones, its past practice of crediting each customer’s account for unused cellular data. Instead, it cut its rates for plans offering 1GB and 2GB of cellular data in addition to to unlimited voice and texting. Formerly, the 1GB plan was $25 monthly; now it’s $20. The 2GB plan was $40 monthly; now it’s $30. And there are higher plans, including a $45 per month 4GB plan, which replaces an older $55, 3GB plan.

The company says it is focused on the 1GB and 2GB plans, as that is where its typical customer’s cellular data usage falls (partly because they mostly use Wi-Fi data.) The plans are less expensive than those of the major carriers, at least at lower data volumes. For instance, for 2GB of cellular data, T-Mobile charges $50, although the comparison is muddied by T-Mobile's free music streaming.

Also, there’s more competition in Wi-Fi calling than there was in 2011. For instance, all the cellular carriers offload calls to Wi-Fi where possible, though Republic asserts that they aren’t truly Wi-Fi first, or by default. Phones are built to allow this, and T-Mobile in particular has relied on this practice.

And then there’s Republic’s new, potentially giant competitor, Google’s Project Fi. This service also uses Wi-Fi calling, but not necessarily by default. It puts your call on the network it deems best, including Sprint and T-Mobile. Fi also sells cellular data at $10 monthly per gigabyte, and gives refunds for unused cellular data. But it has a big downside: it only works with three of Google’s own newest Nexus phones.

Finally, there’s the iPhone. Republic doesn’t work with iPhones, even though carriers like AT&T and T-Mobile support Wi-Fi calling on iOS. The company is hopeful, but uncertain, that that may change with iOS 10, which allows VoIP calling services to be treated more like cellular services. But Republic is wary that Apple will give it the amount of default control it has on Android, and feels it needs.

I can recommend Republic for people who want lower, predictable bills, who are in Wi-Fi environments for much of their day, and are fine with Android.

The real question, to me, is why there are so few other choices in Wi-Fi-first calling.