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The family's real rise to prominence began in the early 14th century, when they managed to be included among the patrician families that held the hereditary right to be members of the Great Council of Venice following the so-called "Serrata" ("Closing"). As membership in the Great Council was a prerequisite for holding any of the senior offices of the Republic of Venice, this meant that henceforth the upper nobility monopolized control of the state. The first important member of the family was Niccolò, who owned much property both in Venice and in the hinterland ("terraferma"). His contacts with the princes of northern Italy led to him being knighted by Cangrande I della Scala, Lord of Verona, in 1328, while three years later, he was enfeoffed over his estates at Zellarino, Noventa, and San Bruson and given the hereditary title of count by John of Luxemburg. Niccolò married three times and had two sons, Giovanni and Jacobello, and two daughters, Agnesina and Maria.