I was Googling for reviews on the Denon C560r in-ears, even though I have owned them and have written a review on this very site, and somehow found this review for the A-Jays!!
I have tried the A-Jays Three and Four, and in my opinion, they good for the price, but not great. However, you do get a decent case, and the flat (tangle-free) cable!! If I had to describe them, I'd describe them as a prettier, slightly better version of
Sennheiser's CX300 in-ears, which I have owned.
These IEMs are quite bass-heavy, like most consumer-grade IEMs, but the quality of that bass isn't particularly high. It sounds bloated. The mid-range is too recessed, but the treble is quite good. It's not sparkly, which some people may consider a positive, since they won't fatigue your ears. However, the bass might, since there's so much of it. The sound signature is "V"-shaped (strong bass and treble presence), which makes them appropriate for most rock and pop songs.
Speaking of the build quality, the A-Jays may suffer from the same cable issue after long-term use. The tangle-resistant flat cable, while thicker than the d-Jays' and q-Jays' thin cable, aren't reinforced at the connection point between the cable and earpiece, so they may be like a lot of IEMs and break at their connection points. Also, the flat cables are VERY NOISY on contact (a.k.a. Microphonics). This will affect you every time you walk, or when the cable bumps against your body, table, whatever. Also, they weigh more than normal cables, so they naturally tug and pull downwards (gravity's a bitch....). I don't know of the long-term longevity of these IEMs, but unless they defy physics and common sense, you may need to be quite careful and not tug on the cables too much.
The fit is OK, but not great. If you're moving around, the relatively heavy cable will tug the earpieces out of your ear.
Overall, the A-Jays are very good for the price.
However, if you can afford to pay a bit more, the
Denon C560r and
Klipsch S4i in-ears are definitely better in terms of sound, and they both come with an iPhone/iPod Touch remote. I prefer the Denon C560r because the build-quality is better than the S4i, but the sound quality of both are high.

The popular iPhone-ready Klipsch S4i sound better than the A-Jays, but like the A-Jays, they have un-enforced connections between cable and earpiece. Of course, there's the
Klipsch S5i "Rugged", which sound as good as the S4i but are highly water-resistant (good for the gym) and built better.

IMO, the C560r sound better than the S4i, but that's just a matter of opinion.
Soooooo.....also consider these other iPhone specific IEMs:
-Denon C560R (the C260R sucks)
-Klipsch S5i Rugged
-Klipsch S4i
-Shure SE210m
And FYI, I have owned the JAYS d-Jays, Denon C560r and C260r, Sennheiser (several models), Klipsch S4i, a decent pair of Sony IEMs, and....I forget. Usually I'll either break them, or lose them.
EDIT TO ADD:
HERE is another review (it's not mine).