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

I have 2 pair of Realistic (Radio Shack) Minimus 7s, they're OK. I used one set for surround rears for years on the shelf behind the couch. I seriously upgraded them to Martin Logan Motion 2s (with AMT) These will work on a desktop 110-25000 Hz. Put a $40 CyberAcoustics under the desk to fill in lower freqs. They are worth the $240/pr while they last. Call Safe and Sound and ask if they have any refurbs ($150) laying around.

The holy grail of desktop speakers are the Monsoon Planar 9s. They are like mini Magnapans. The catch is that the controller connects to the amp\sub via a 9 pin mini din and they are All broken. If you can microsolder an old Mac printer cable would work. I have the pin assignments. Otherwise you can jury rig them to another amp/sub (like I did for my TV) but the SQ will probably be inferior to OEM.
If you are ambitious, Madisound is the winner. I love the pair I built from scratch 25 years ago before they marketed cabinet kits. Probably cost prohibitive by the time you match an amp to them. 
Unless you are dead set on your own amp I recommend powered speakers for better SQ and less clutter. Review the rec's above. Even though I have not heard the Vanatoos I'll wager that they sound the best due to bi-amping (matched to the drivers.)and radiators.  Only a direct showdown could prove me wrong.
If you want to max out your $500 my vote is for Vanatoo Transparent One Encore B-Stock.  You'll probably have to make a request to reserve a pair.

Thanks so much. I'm not ambitious to build for desktop. I am open to de-cluttering. The idea of a bi-amped speaker for desktop was something I would have thought overly- fancy for that application, but there you go!

That's why the self powered bi amped Vanatoos look like fitting the bill.
I have an Ascend Sierra for a center in my surround sys. Love it. Blends well with the ML Motion 2 AMT rears and front ESLs.

+1 for the. Vanatoo.  Everything you need save a source device in a compact great sounding package that is loaded with technology.  The tone controls alone will come in very handy. 

I’ve owned and used Vanatoos and kef ls-50’s as desktop speakers, and both are great, but I think the Kefs sound incredible nearfield.  Especially powered with class d.