[General Questions and Answers] Planterz:
Probably. Some sacrifice will have to be made when it comes to your preferences.

If indeed such a phone exists from some obscure brand, I can pretty much guarantee you that it won't have LTE and if by some miracle it does, it'll probably only work on Chinese or other common SE Asia bands. It'll also most likely be a hunkojunk.

I mean the phone is exclusive to a specific carrier. In the US (and Canada - don't know about Mexico or Central America), typically a customer buys a phone "on contract" which means they only pay a fraction for the phone up front (or even get it "free"), and the remaining cost of the phone over the next 2 years as part of the monthly bill. To entice customers to switch or stay with them, carriers will contract manufacturers to produce a phone to their own specs. The Droid line, for example, is exclusive to Verizon.

That's what I said. :confused:

The Droid Mini is quite a nice phone. It's actually smaller than your Ace 3 (same height, but thinner and narrower). The kevlar body is awesome. I especially like the way the red one looks. It has the same speedy internals that the Moto X has, and owners of the Moto X are typically impressed with how quick it is, despite being "only" a dual-core 1.7GHz S4.

But being exclusive to Verizon, it only works for them. Although, theoretically, since all Verizon phones are "World Phones", it should work outside the US on other networks with the right SIM, but the catch is that you'll only get 3G speeds (maybe only 2G). You can get one new off eBay for $250, less for used. From what I understand, you don't need it to be unlocked, since once you've put a SIM in from another country and use that SIM's network, the phone will be "unlocked".

The Rezound was also Verizon specific, so it'll have the same limitations outside the US as the Droid Mini. It's also quite old, but frankly, its specs aren't that shabby compared to many low-to-mid end devices these days. And you can get one for $130 off eBay.

The HTC One Mini (M7) isn't a bad phone, but it's only "mini" compared to the full-sized M7; the front-facing speakers, while cool, make the phone pretty large despite the 4.3" screen. Don't bother with the M8 Mini. The specs are mediocre, and it's basically the same as the full-sized M7, which has far better specs and a larger, superior screen. The M8 Mini does have the microSD slot though.

The best/newest of them is the Xperia V, and it's about 2 years old. Nice phone though, if a bit dated. Updatable to 4.3, LTE on bands 1,3,5,7, 42.2Mb/S HSPA+, dual core S4+ 1.5GHz, microSD slot, and 13MP camera. It's a bit chubbier than you're looking for though. $200 on eBay. The Xperia SP is only a bit bigger (but thinner) than the V, and has newer specs and .3" bigger screen.

The Xperia Z1 Compact is the best small Android out there. Its specs make absolutely no compromises. It also works on 8 LTE bands, so no matter where you go in the world, you should be able find prepaid SIM that'll work. But you're definitely paying for it; $420 on eBay. Cheaper than its bigger brothers though. Perhaps when the rumored Z3 Compact comes out (September?) the Z1C will drop in price.

What country are you in, and what provider do you use? If I knew what LTE band(s) you'd need, I might be able to help you further.