Best small, desktop speakers, $500 or under (new or used)

Many more good suggestions — thanks!
Wharfdales have a down-firing woofer — that’s helpful to know, because the rear of these speakers need to be about 1-2 feet max from a wall.
Will look at again at M Audio and Audioengine.
@axpert: environment: small office, about 11x14 150 sq ft., 7.5 ft. ceilings; nearfield listening, 2-3 feet, speakers to ears; speaker rear to wall would be 1-2 feet max. Type of music preferred, classical, jazz, but rock too. I.e., varied.
Go listen to a lot? In the time of social distancing? No. I am content to buy a good speaker or find a good value based on reviews or used. This is for listening to music at a desk. I can’t get wrapped up in comparisons, though trying 2 pairs could be fine. I can learn to like a lot of things for office listening.
Why do people sell speakers? Many reasons. Doesn’t worry me. Speakers are a very stable technology, so this seems a very low-risk purchase.

Let me add a detail that may be helpful. A friend lent me some Paradigms once and the Minis were too big and the Atoms were the right size.
Dimensions here made a difference. Viz.,

PARADIGM MINI
H 13.4 x W 8.3 x D 11.4

PARADIGM ATOM v.6
H 10.6 x W 6.7 x D 8.7

I have to add -- reading the reviews of the AudioEngine and thinking more about some suggestions here to clean up the desk area -- the Audioengines are enticing. I could be persuaded to give that Adcom stuff to my kid...

For office desktop I would go powered speakers to clean up the area, less wires as well. What are you using for a source? Some like these Fluance can connect to your computer with USB. 

https://www.fluance.com/powered-2-0-bluetooth-active-6-inch-bookshelf-speakers-white-walnut#!prettyP...

Get a pair of Google Home Max speakers. They can be paired wirelessly and they sound awesome. You can disable the mic for the Google assistant and can cast music directly or use it as a Roon endpoint. Aux in is available as well.

One thing these have is the ability to tune themselves depending on the environment they are placed. All for about about $400 a pair!

I use a pair of these on my desk everyday and I am constantly reminded of foolish my decision was on getting the LS50W.

You can easily build "the best small speaker I've ever heard" according to one Stereophile reviewer. It uses the SEAS tiny L12RE-XFC co-ax driver.
I built the cabinet recommended by SEAS and put the speaker into it. The speaker itself was $165 or so each. I bought four. I used a sealed cabinet made of counter top material for one pair and the recommended cabinet design for the other pair. Not much difference in sound. The sealed cabinet is very easy to build; use the same outer dimensions as the recommended cabinet. I've used engineered quartz (recommended) and granite (it can crumble in your hands and is NOT air tight) for cabinets.

Madisound sells the speaker and M'sounds own fancy crossover (mount externally). Broken counter top material is cheap and the shop will cut it for you. The cabinet will be acoustically inert. Make the front piece from some nice wood and glue it on with the speaker mounted on it. MDF on the rear, cut to fit flush with the counter top sides and bottom. You're out for less than $600 per pair with nice terminals. A subwoofer never hurts, but they will surprise you running "barefoot."