A Vatican tribunal agreed Monday to let the defense call some of Pope Francis' top advisers, including his secretary of state, to testify in a trial over leaked documents, as the Holy See sought to quash criticism that the five accused weren't getting a fair trial.

Judge Giuseppe Dalla Torre also agreed to defense requests to admit more complete text messages and emails, as well as letters of recommendation and the results of a monsignor's psychiatric exam into evidence as the trial got underway in earnest.

Three people affiliated with a papal reform commission are accused of leaking documents to two reporters who published blockbuster books detailing waste, mismanagement and greed among some cardinals and bishops, and the resistance Francis is facing trying to clean it up.

The two reporters are also on trial, accused of having illegally acquired and published the material -- accusations that have drawn criticism from media rights groups around the world.

Francesca Chaouqui, an Italian communications expert and commission member, had called as witnesses three of Francis' top advisers, including his secretary of state, Cardinal Pietro Parolin.

Dalla Torre admitted them all, overriding the prosecutors' objections. It remains to be seen, however, if they can be compelled to testify; Parolin, for example, could argue he enjoys immunity as a head of state.

During the first hearing Nov. 24, Dalla Torre's court had seemed intent on wrapping up the trial as quickly as possible, refusing defense requests for more time to prepare, rejecting requests from the defendants to allow their longtime lawyers to represent them, and scheduling highly unusual, back-to-back morning and afternoon sessions all week.

But by Monday, Dalla Torre seemed much more even-handed and ready to let the trial take time.

Last week, amid criticism by the defendants that their rights were being violated, Francis himself acknowledged that he had wanted the trial finished by the Tuesday start of his Holy Year of Mercy. But he said he realized the defendants must have their rights respected.

Responding to the criticism, the Vatican spokesman, the Rev. Federico Lombardi, issued a statement Monday entitled "Guaranteeing a Fair Trial," in which he insisted that the Vatican legal code was on par with other countries, that the defendants' rights were being respected, and explaining that only lawyers specially trained in Vatican law could appear in the tribunal.

Chaouqui, however, has noted that exceptions have been made in the past, including for her long-time lawyer who was nevertheless denied admission for this trial.