the 2012 has the tech package, which has 4k worth of upgrades on it. if i were to buy this one brand new it would be at least 22kHave you researched the trims and options of that Veloster and what that car's MSRP was? The site says it has a DCT, in which case it may have been the lowest-trim Veloster, whose MSRP right now is 18k. It may have had a few options, but I can't imagine the car's MSRP having been above $20k.
I expect a lot more than ~$4k off of a 3/4-year-old car with nearly 40k miles. The car was probably a 3yr/36k lease return, whose residuals almost never go above 60%. And if it was a lease, it means the original owner probably had no intention of keeping it or taking care of it (beyond the bare minimum). I wouldn't value that car for more than $10-12k.
If you're in the $15k range already, why not shop for a new car? There are lots of sub-compacts that can be had for under $20k. New Civics start out at $18.5k. Fits are much cheaper.
In general, new cars can be had for their MSRP price, out the door. That is, you can usually talk the sales price of the car 10-15% off of MSRP. The sales price of a new Civic could be as low as $16-17k, which is barely more than your current price (for a better car). They won't be as well equipped, but you'll get better financing, and the car will be brand new.
EDIT:
If you really like the Veloster, get a few quotes on a brand new one, and see how that compares to your current price. If after that, you're still set on the used one, you can leverage the new quote to get an even better price on the used one:
"You're trying to sell me a used 2012 model with 40k miles for $15.5k when I can get a brand new 2016 model for $18k?"
edit: but i will indeed call around.