How do dim screen, even if artifically, below the minimum?

With xrandr you can affect the gamma and brightness of a display by altering RGB values.

From man xrandr:

• --brightness

  Multiply the gamma values on the crtc currently attached to the output to specified floating value. Useful for overly bright or overly dim outputs. However, this is a software only modification, if your hardware has support to actually change the brightness, you will probably prefer to use xbacklight.

I can use it like:

xrandr --output DVI-1 --brightness .7

There is also the xgamma package, which does much of the same, but...

• man xgamma:

  Note that the xgamma utility is obsolete and deficient, xrandr should be used with drivers that support the XRandr extension.

I can use it like:

xgamma -gamma .7