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

So, did you get enough opinions? You are probably more confused than when you started. The reality of the situation you describe really has no good answer. What is the environment - - -? What volume do you expect to play them at. 3' is really "nearfield" so I assume office. And more important, what type of music do you primarily listen to. If you have to play the speakers at moderate to low volumes, there aren't many inexpensive speakers that do that well. I would suggest making a list of the suggestions in this blog, and see if you can find a place or places near to you, to audition as many as possible. For the past 2-3 years the industry has been turned on it's ear by some of the so called, entry level bookshelf speakers by ELAC. Assuming you are not looking for powered speakers such as AUDIOENGINE, the ELAC B 6.2 currently at $244 /pr. is pretty hard to beat. However there are Wharfedale, and Klipsch speakers in that same price range. You just need to listen to them They all sound different. I'd stay away from used. Or, I'd certainly ask "if your speakers are so good, why are you selling them" ? I think you get my drift.

Totem Kin Mini Monitors. Or anything small from Totem

The Elacs and Wharfedales are great; I mentioned them.

I’ve seen them for sale Used so your argument doesn’t hold up

MAudio BX5s while powered, are a great little desktop monitor. Put out a great tight image with impressive low end. Plus, you can add a sub to them if you want. Great bang for the buck for a powered monitor.

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