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

Another thing too, if you buy a pair of Adam A5x’s used at $500 and sell your adcom gear for $250, you’re only in it for $250. Powered monitors are going to clean up the look at volume controls easily accessible on the speakers might be a plus over the adcoms.

Some swans or edifiers might be a consideration as well but 
Adams are definitely the real deal though.  You need to know that with these powered speakers you are getting 4 amps, so think of it as dual mono blocks.  Each driver has its own amplifier, picked out but they speaker designer to perfectly pair with the speaker that they designed.  Also, they don’t have conventional crossovers.  The crossovers are all handled in the digitail domain.

I have the powered Audioengine 2+ in a gorgeous glossy red finish with a cheap powered sub on the floor. All on closeout and total price under $500. They blow me away with any halfway decent recording on YouTube. Or just everyday spoken voice.
Plenty of exotic mini-stuff out there, but with this setup I am in heaven when working on computer, which is half the day.
Note, be sure to buy the optional stands which position the speakers toward your head. Under $30 if I remember right. 
If it's something you need to look at every day, get these. Endlessly beautiful in sight and sound. And damn near free.

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