It's getting hard to define premium headphones. Once they were the ones that cost more than $200, but these days there are headphones that cost as much as a BMW. The guy at my local hi-fi shop says most customers spend between $500 and $700. Does this make $200 headphones cheap? I guess it depends where you shop.

Should premium headphones be defined by sound quality rather than price? This leads to a vexed question: can Bluetooth headphones be premium? Bluetooth is getting pretty damn good with the aptX codec, but there are still purists who hold that any headphones lacking a cable are for people who wouldn't know a Stradivari from an air guitar. They're just as scathing about noise-cancelling headphones.

They must be wringing their hands in frustration right now. Bowers and Wilkins, that most frightfully British of speaker-makers that became legendary with its windswept Nautilus – the only speaker I've seen used for album cover photography – is now making Bluetooth, noise-cancelling headphones. This must be leaving audio purists with the same gutted feeling that car enthusiasts experienced when Alfa Romeo dropped clutch pedals.

OK, I admit that while those early clutch-free Alfas were frightful they've improved since, but they're still not as good as manuals. And, depending on your ear, the B&Ws may still have a way to go too.

They're called PX, they cost $550 and they're nicely thought through. Previously I've railed at headphones that automatically turn off and on and do other cute stuff when you brush or tap the earcup, even by mistake, but these limit such ideas to what you need without mucking it up with stuff you don't. Lower them around your neck, or just lift an earcup, and the music stops. Put them back on again and it resumes. It works. The three-level noise cancelling is also clever. Two levels provide light cancellation so you can hear the traffic or talk to people, the one for flying is heavy. All of this is adjustable with an app that I couldn't download without buying a new iPad.

The PXs are comfortable, with soft earpads that mould to your head nicely and a tightish clamp pressure that's good for dancing. The cups are large enough to contain an average ear without annoyance, but if you have large ears it becomes a close thing.

You'll note there's a slight drop-off in bass when you switch to noise cancelling, although I heard this more as a welcome increase in mids and highs. Without cancellation the soundstage widens a bit too. I preferred the sound with the cancellation turned off, but it certainly wouldn't stop me using it inflight.

Either way the PXs are heavy on bass. The first track I tried was Gordon Lightfoot's If You Could Read My Mind and for the first time the guy plucking the bass was the hero. It was the same on Bluetooth aptX. I switched to Oppo PM3s ($599) and he returned to the background where he belonged. My Bose QC25 noise-cancellers, now no longer available, are pretty bassy too, but compensate for this with more airiness than the PXs.

Of course the QC25s lack Bluetooth, and the Oppos don't have that or noise-cancelling.

If you like bass but regard Beats as way over the top, these are great headphones; spacious, defined and full bodied. But listen closely to a few favourite tracks before you make up your mind because their sound is very particular. It has ever been thus with B&Ws.