While at the council he wrote his "Decem libri orthodoxarum explicationum" (Venice, 1564, 1594; Cologne, 1564, 1574) against the work of Martin Chemnitz, "Theologiae Jesuitarum praecipua capita".

Chemnitz answered by his well-known "Examen Concilii Tridentini", in reply to which Andrada produced his best work, "Defensio Tridentinae fidei" (Lisbon, 1578 and 1595).

Posthumous were his Defensio Tridentinæ fidei (1578) (remarkable for its learned statement of various opinions regarding the Immaculate Conception), and three sets of his sermons in Portuguese.

Payva de Andrada had not only a grasp of theological questions which won for him an important position among sixteenth-century theologians, but he was also so clear and convincing in the exposition of his arguments that he proved an admirable apologist, and it was matter of regret that his death prevented the completion of his great work, the Defensio Tridentinæ fidei This had progressed as far as the fifth session, inclusive of the doctrine upon the Immaculate Conception in defense of which it marshalled an imposing array of authorities.

His nephew, Diogo, the younger (1586–1660), produced Chauleidos (1628) and other Latin poems, including sacred dramas, and a moral tract, Casamento Perfeito (1630); he also shone as an historical critic.