ATC and Loki

The downside to low level listening to accurate speakers is a lack of bass.  It only sounds right if you're listening at levels closer to realistic for a real performance.  

"The downside to low level listening to accurate speakers is a lack of bass."

I respectfully disagree. I suppose you've auditioned all the "accurate" speakers available today. Just because good active speakers, made by folks that also serve the recording industry (pro audio) have much greater dynamic range potential than most conventional speakers does not mean that they all are lacking at low listening levels.

It seems to me that the definition of high-end audio is the most accurate reproduction of the source at least it was at the beginning. Of course that reveals any issues upstream. Rather than addressing these issues, the speaker is blamed for being "too accurate".

So many spend lots of money on less than accurate speakers with anomalies to suit their taste. Low cost, distortion generators can do the same for far less money.

If your taste is less accurate, euphonically colored sound, nothing wrong with that. My argument would be, you don't have to spend a lot of money to achieve that, really a fraction of what a highly accurate system that excels in tonal correctness, presence and unrestricted dynamics would cost.

When you have this problem with "accurate speakers", the most likely cause is a poor amplifier speaker match and/or improper speaker/listening position set up.

Yes, I can see how the OP's speakers could sound the way he describes. But being intimately familiar with the current revision of this speaker, it's definitely not the fault of the speaker. If you have the original version, then yes, the tweeter was less than optimal and that is where a device like the Loki (very cost effective and well designed) may help. Personally I would prefer a Manley Massive Passive but that's like 100 times more expensive.

I don't mean they lack accurate bass, just that they sound like they do at low listening levels.  It only makes sense for accurate reproduction at inaccurate levels to sound inaccurate.  It is inaccurate.  You can make it sound more accurate by countering the level distortion with frequency response distortion but true accuracy would include accurate volume.  A lot of speakers have some exaggerated bass, at least at low volumes, and they sound better at low volumes because of it.  

Who are they? Which ones have you auditioned, set up and powered properly?

Exaggerated bass at any volume, which will compromise sound quality at higher volumes, is not the solution.

For those that can not or will not solve the problem properly, I would much prefer a good equalizer which can be adjusted at low volumes than a speaker that is designed to have exaggerated bass at low volumes.

BTW, another equalization option is a very good sounding 6SN7 based line stage with useful equalization, especially in the bass region and fun spatial controls both of which can be bypassed. Black Ice Audio Fusion F360. They also offer these circuits in a stand alone device that can be inserted in your tape loop, Foz SS-X.

Just be aware that such things are not approved by the audio police.