What makes a speaker sound great at low volume?

The one thing that helped my system in low level listening was the use of a autoformer or a transformer volume control . Check out the Dave Slagle Intact Audio site .

Please..it's BASS, not base...unless we're talking about footers or stands or fans...BASS. Thank you. Also, looking for low tones in audio is called Bass Fishing...they have tournaments...here's a thing, my Schiit Freya has a clicking yet interesting "128-step relay attenuater" that purports to keep levels equal in each channel at any volume and it seems to work. And that Loki...can't say enough about how well it works, although maybe I just did.

Among many many parameters, I'd say the single most important one is the speaker itself. I own several, and I find that usually, bookshelves sound the best at low volumes. If your room is not that big, I would look that way. I have 99dB (Tannoy Westminster GR), 95dB (Tannoy GRF90 GR) and 89dB (XTZ Divine Alpha) speakers. All quite different types, and the Westminster clearly being the best speaker, but the XTZ Alpha sounds far better at lower volumes, and costs 5 times less. It also sounds very very good at high volumes actually, and in my view betters many 20k to 30k speakers out there... I highly recommend that speaker. It also has tuning possibilities to suit taste and/or room.    

hddg, been looking at XTZ, seems like a great value just don’t see anyone carrying them in the States. Are you in US?

You may be barking up the wrong tree.  HE speakers are specialized and have compromises that not everyone warms up to.  
All other speakers of normal to low efficiency will come alive at lower volume with proper amplification.  
Class D amplifiers tend to sound thin and weak at low volume levels.  Higher powered Class AB amplifiers will do the job nicely.  I used to run a 150 watt / channel NAD amplifier and I was simply amazed at how incredible the bass in a typical mid efficient tower speaker sounded at low volume.  
Get yourself an amplifier with some guts and you will be all set with the speakers you already have.