[1] Beginning with Karl Hopf in the 19th century, several modern historians held that Andrea's father had seized the Aegean islands of Santorini and Therasia following the Fourth Crusade, meaning that Andrea was the second lord of the island following his father's death c. 1245,[1] but this has been refuted in the later 1960s, when it was shown that Barozzi rule over Santorini can be documented only from the early 14th century on.
At that time, he negotiated a treaty to end the War of the Euboeote Succession, between the Triarchs of Negroponte, who had been backed by Venice, and William II of Villehardouin, the Prince of Achaea.
[1][4] Shortly before, when military operations were favorable to Villehardouin, Barozzi tried to change the course of the war, in an overwhelming victory in a battle near Chalcis and trying in vain to besiege Oreoi.
When Barozzi took the bait and moved east to pursue Grillo with his much larger fleet, the latter was free to attack the Venetian convoy off Saseno, and capture it almost in its entirety; only the giant merchant ship Roccafortis escaped.
Barozzi did not hesitate long: he not only captured the Oliva, but also began a siege of Tyre itself, in the hopes of depriving Genoa of access to this, the second-most important port city of the Levant.