About what percentage do the LEDs seem to be at when the dimmer is all the way down?

The entire problem is that they cannot be made to behave the way incandescents do. Instead, the best I've seen with simple parts is dimming down to about 30%; full off only by removing power totally; then when you restore power you have to raise the control output until they suddenly pop on at about 50% or more.

I've seen just one killer system, but we had to start from scratch with the wiring and even the conduit runs. Crestron controlled a DMX lighting controller. Its 0 - 10V output fed a Lutron magnetic circuit dimmer; the Lutron outputted an AC voltage that dimmed all the way to zero; each such circuit had a 120V - 12V power transformer, a full-wave bridge rectifier, and a large filter capacitor. And even this had visible dimming steps near zero, despite there being 1024 distinct ouput levels. And who's going to install an 8x8x8 NEMA box near each light circuit?

Edit: I just realized I forgot to say that the bulbs we used were 12 volt LEDs, in the range of ten watts each. If I remember correctly, about 400 watts illuminated a room about 60 feet by 40 feet. It was bright enough for a theater, not quite bright enough to comfortable read in.