Yes, I know! At the time the Italian army was viewed as superior to the German Army. (Yes hard to believe but it was believed back then!). There was no way Hitler could intimidate Mussolini into giving up south Tyrol. Italy spent a lot of lives in WWI in Alpine fighting. South Tyrol was its reward for doing so.
Italy also got Trieste and other areas along what is now the border with Slovenia from Austria, as well as Zara (now Zadar in Croatia). Zara had been a base for the Austrian navy. Georg von Trapp (the father in “The Sound of Music”) was born in Zara when his father was in the Austrian navy. The Italians wanted more as their reward for siding with the Allies in the war, places where few of the inhabitants were Italian—Woodrow Wilson opposed them.