In reply to brianrunner:
Wild camping is not allowed within the Brenta Adamello Natural Park (which means nowhere in the Brenta). This also applies to most popular Dolomite areas.
However, there is an accepted tradition of bivouacking overnight. Exactly whether you are allowed to bivouac beside a hut is a grey area, as is putting up a tent.
People do this occasionally (put up a tent in the evening, take it down in the morning) and it seems to be accepted by and large. Leaving a tent pitched stationary will lead to you being told to move on, if anybody notices it and can be bothered.
There are parts of the Brenta where you could camp for a week and never see a soul, but those are the same areas that bears roam. Also, if you were spotted in such places (say from a helicopter) the authorities might get genuinely alarmed thinking you are poaching or up to something bad, and send in the rangers. At that point you really are risking a fine.
You are allowed (obviously) to sleep in bivouac shelters and these are generally quite comfortable. Not so many in the Brenta but certainly a few.
In the wilder corners of the Dolomites these are the only option, typically good, and again you could live in them for a while and hardly see a soul.