While the TDM don’t have ANC, they do have relatively firm earpads and a tight fit that blocks out noise the old-fashioned way: with noise isolation. Unfortunately, maybe for this very reason, the earpads are not as plush as I’d like, and the whole thing feels tight on my admittedly large skull and less than dainty ears. It’s not eerily quiet like using the best noise-canceling headphones, and I can’t imagine that’s a compromise many users are willing to give up easily.

At 11.9-ounces, the Neo are also heavy for on-ear headphones. It’s no surprise, given that they’ve got four 40-mm drivers inside, but it is noticeable. For comparison, they’re 3 ounces (or 34 percent) heavier than the Sony WH-1000XM6, 1.9 ounces heavier than the more affordable Soundcore Space One Pro, and a full 4.25 ounces heavier than the on-ear Beats Solo 4.

The Neo sound detailed and pleasant, with clear bass and appreciably distinct vocals, but the presentation feels quite boxed in. Music lacks the scale and openness I expect from great headphones, and individual instruments are crowded for space. If they were comfier to wear, I think I’d enjoy the audio a bit more, but I found it all quite tiring, and certainly not on a par with similarly priced alternatives.

They are not awful, but they do feel compromised, and given the price, they also present a bit of a quandary for travel. You gain a Bluetooth speaker at your destination but may spend the journey wishing you'd packed more comfortable headphones with proper ANC.

Just to reiterate, I really like the engineering and execution of the Neo, and I love how small the headphones can fold away. The Bluetooth speaker looks cool too, and it gives the headphones a second function. Sadly, the TDM can’t compete with the best Bluetooth speakers I’ve tested.

There's enough volume for casual listening, but the sound is thin and underwhelming. It keeps pace with the tiny-but-mighty JBL Go 5, but given that it has twice the power and double the drivers, it really should sound better. I also played it alongside my favorite current portable speaker, the $120 JBL Flip 7, and the difference between the two was like racing a speedboat and a paddleboard.

Having a Bluetooth speaker on hand whenever you have your headphones is convenient, and the ability to share a song instantly might appeal, but compact Bluetooth speakers have become so good that the TDM’s subpar audio quality is hard to ignore.

Photograph: Chris Haslam

The obvious benefit to the Neo is having just one device to carry and charge. But is that enough to justify the compromises?