Anonymity is a convention at L'Osservatore. Mr. Agnes refuses interviews altogether, and other editors talk only if their names are kept off the record. The secrecy even extends to the readership; circulation figures are not discussed openly. ''I myself don't even know,'' one editor said, looking stricken that he was being asked the question.

In fact, the Italian-language daily, supported by ever-increasing subsidies from the Holy See, has a tiny circulation, far less than Italy's other major Catholic daily, Avvenire. The official circulation figure for the Italian daily is 20,000, but it has not been confirmed by an outside audit. At the paper itself, some say readership has slipped below 10,000, behind both the Spanish-language and the English-language weekly editions.

There was a time when the daily paper, which now has an average of eight pages, had greater weight. Its circulation peaked at 150,000 in late 1939 and early 1940, when it was the only Italian-language paper to print military bulletins from all sides in the opening phase of World War II.

Even now, the paper prides itself on its attention to foreign news, particularly reports from the developing world that are ignored by the mainstream Italian press. In recent weeks, L'Osservatore devoted the top of its front page to the refugee crisis in eastern Zaire.

A former reporter for L'Osservatore, now a correspondent for Italian state television, remembers a time when the Pope himself followed the paper's coverage closely. ''Pope Paul VI used to read the paper cover to cover,'' Luigi Saitta said, recalling one hot summer afternoon at the height of vacation season when the Pope called to complain about a rash of typographical errors.

Pope John Paul II, a native of Poland who came to the papacy with media ambitions beyond newspapers, is said to show less interest in the daily paper, and it is probably not coincidental that a Polish-language monthly started up shortly after he took office. The collapse of Communism and the weakening of Italy's Christian Democratic Party have undercut the influence of the paper on Italian politics.

''It's a very valuable documentary service,'' said Father Thomas Reese, an American Jesuit scholar and author of a recent book on the Vatican, ''but it is also a wonderful cure for insomnia.''