It was my understanding the btr3 had 64 step volume control while the newer btr3k has 32 step volume; this is for me is a disspointment.

I am terribly sorry as this is my mistake.
BTR3K and BTR5 are 60 steps and BTR3 is 32 steps.
I am correcting it.
Please refer here
https://www.head-fi.org/threads/fii...h-fidelity-bluetooth-amp.928317/post-15535149

Thanks for pointing it.

Considering entering into world of bluetooth dac/amp.

Is there a sound quality improvement using my sub-$50 chifi IEMs with BTR3K versus plugging IEM directly into my smartphone (S10+ Exynos)?

To tell you the truth it doesn't worth it for cheap chifi iems as S10+ phone out is already good.
First upgrade to a better iem with a balanced cable and then yes the BTR3K will be a leap in performance.

Thanks Ichos. Appreciate the reply.

I'm thinking about pairing one of these, or perhaps the BTR5, with a new pair of IEMs (which I haven't bought yet, either the Fearless S8F, the ThieAudio Legacy 9, or the FiiO FH7). I know that powering any of those IEMs wont be an issue...I'm just trying to use the BTR to improve sound quality vs direct plugging into my iphone and for easier connectivity (so I don't need to mess with the headphone to lightning dongle). I was already planning on spending $150 on the Audiolab M-DAC nano until I saw that nobody on head-fi seems to have written about it and everyone loves the BTRs, so I wouldn't mind spending the money on the BTR5. But I do prefer the size factor of the BTR3k. Is the sound significantly better with the BTR5 that it's worth being a little less portable?

And, as someone who's never owned balanced headphones, should I try and get these headphones as balanced? What does that even exactly do? haha. I love good IEMs (have had my FLC8s for a couple years now) but I am far from really understanding hi-fi gear. Thanks!

Hi , both BTR3 and BTR5 sound slightly better from the balanced out as they are designed fully balanced.
So it is better to invest in a balanced iem.
BTR5 is better especially in technical performance but not by a that great margin so in my opinion judge first from a form factor view.
If you don't mind bigger then yes go for the BTR5.

I agree with Ichos about balanced cables; I let my ears decide and there is a noticeable differnce.