Best month to hike in the Dolomites?

My wife and I are going to do some hiking in the Dolomites. We are thinking of either of June or September? Our experience in June in Switzerland was that there was a fair amount of haze in the air which made for less than optimal viewing. Does anyone have an opinion they can share about this issue.

TIA.

A couple of years ago, my son and I spent some time in the Dolomites in late Sep - early Oct. We did some hiking, but mostly climbing and via ferratas. Overall the weather was excellent, perfect temperatures, clear skies or mostly clear. We did have a couple days of pouring rain (hey, it's the Alps! What do you expect at any time of year? Besides, Alpine storms are really neat, summer or winter, if you are equipped and pay attention).

Some photos, from the first two weeks in October -

Sign on the Agatha Christy Weg - one of her stories has the climactic scene in the Labyrint

A chamois

Marmalata and Boe from the top of one of the via ferratas on Masere. One of the v.f. on Marmalata is referred to as the "Cliffhanger", because part of the Cliffhanger movie was filmed there.

One of the things about the late Sep-Oct time frame is that it is after most of the tourists have left, so hotels, B&Bs, and such are a bit cheaper (well, relatively - nothing is really cheap there, especially with the US$ weak compared to the Euro).

By the way, you will find that German (with an Austrian accent) is more useful than Italian throughout the Dolomites, though both are spoken by many (including the areas where the language is some variant of Ladino - mostly small villages in isolated valleys).

Thanks for the nice pictures and the helpful advice.