It was Eldizio's sons, Lamberto and Ubaldo I, who brought the family to the height of its influence in Pisa and Sardinia.
The Visconti of Sardinia continued to take a part in Pisan politics to the end of the century, but their influence there was greatly diminished after 1213.
In Sardinia, Eldizio had married a daughter of Torchitorio III of Cagliari, who became the mother of Lamberto and Ubaldo.
In 1207, Lamberto married Elena, the heiress of Barisone II of Gallura, thus securing control over the northeastern corner of Sardinia with his capital at Civita.
Through advantageous marriages, Lamberto's son, Ubaldo II, secured power in Logudoro for a time.