I came across this post at CultofMac that explained how you can set your Mac’s volume to “ultra-quiet” via a combination of lowering the volume all the way, then hitting the mute key on your Mac’s keyboard. This sets the volume to a barely audible level. The problem of course is that it’s barely audible.
Adjust the volume by quarter bars at a time
Instead, just hold down the Shift + Option keys while using the Volume keys on the keyboard. This will allow you to adjust the volume (up or down) by quarter bars at a time, instead of full bars at a time.