He corresponded with Francesco Betti, a Roman of noble family, who advised him to come to Basel and lay his difficulties before Fausto Paulo Sozzini (Socinus).
Pucci regarded all creatures as imperishable; Sozzini denied the natural immortality of man, treating a future life as a conditional privilege.
He had publicly maintained an extreme form of Pelagianism, printing theses, ‘De Fide natura hominibus universis insita,’ in which he claimed that all men are by nature in a state of salvation.
At Kraków he fell in with John Dee and Edward Kelley, who initiated Pucci into their angelic experiences; and about the middle of 1585, despite objections from Sozzini, he accompanied them to Prague.
Dee and Kelley suspected him of bad faith in treating against them with Roman Catholic ecclesiastics; he exculpated himself in a letter of 17 September 1585, which was printed.
Reverting to the theme which had caused his expulsion from Basel, he printed a treatise 'De Christi Servatoris Efficacitate in omnibus et singulis hominibus .... Assertio Catholica,' &c., Gouda, 1592, with a dedication to Pope Clement VIII.