Harald Bluetooth was a 10th-century king of Denmark. In 1997, an Intel engineer who’d been reading about Scandinavian history proposed borrowing Harald’s nickname for a short-range wireless standard that was then under development within the tech industry. Harald was picked because he is recorded as unifying Denmark and Norway, much as the Bluetooth technology was meant to unite the phone and personal-computer industries. But in the way the public can’t seem to make up its mind about Bluetooth, it’s also fitting that this particular king shares space in medieval lore with a fictitious prince of Denmark, the one immortalized by Shakespeare as Hamlet.

To listen on Bluetooth or not to listen on Bluetooth? That, if you’ll forgive the obvious reference, is the question that many music fans have been asking lately. The issue was brought to a head in early September, when Apple announced it would be doing away with the traditional headphone jack in the iPhone 7 and releasing new wireless headphones called AirPods, which are powered by Bluetooth technology and boosted by an Apple-formulated W1 chip. But Bluetooth audio is hardly just the concern of Apple users. In fact, Bluetooth headphone sales recently overtook non-Bluetooth for the first time, according to market research firm NPD Group. The clever old king has extended his rule.

The ascendance of Bluetooth for music, though, has drawn criticism. “I would not use Bluetooth,” Apple co-founder Steve Wozniak declared in August. “I don’t like wireless. I have cars where you can plug in the music, or go through Bluetooth, and Bluetooth just sounds so flat for the same music.” From the tech press to alt-weeklies, qualms about Bluetooth audio quality seem to be hardening into conventional wisdom.

Are Bluetooth’s critics right? The answer, as with so many aspects of audio equipment, is “it depends.” On a purely technical level, the amount of sonic information that can pass through traditional Bluetooth is less than through wired headphones or even a Wifi connection, meaning lower-resolution audio. So, yes.

But newer Bluetooth variants can allow more data to pass through, providing for sound that can be near CD-quality. What’s more, the decision between Bluetooth and wired or Wifi headphones is only one variable among many that can affect sound quality, audio experts say. In fact, the shift towards Bluetooth may be best understood in the context of music’s growing convenience, which has usually but not necessarily coincided with a loss of audio fidelity.

“Having these kinds of conversations seems more theoretical than anything else,” says Michael Greco, global brand director for audio equipment maker Sound United, which sells wired and wireless products alike. “There’s not a general rule.”

OK, but let’s get theoretical. If you listen to song you know well side-by-side on Bluetooth versus a properly wired setup, you’ll notice an unmistakable drop in quality, Greco and other experts tell me. “You don’t have to be an audiophile to hear the difference,” he says. Anyone who has heard a classic record at a high-end audio store and who also uses a Bluetooth device can probably recognize this as true.

That said, the amount of music lovers whose daily listening occurs via the kinds of stereo set-ups that populate high-end audio stores is fairly small. Even among those who do, what about when they’re going for a run? Wireless headphone sales are up for various reasons, Brad Russell, an analyst at market-research firm Parks Associates, tells me, including lower prices and longer battery life. “More importantly,” he says, “customers are purchasing multiple pairs of headphones to accommodate different use cases.” So you might listen to one set of headphones while working out, and another on a long flight.