At a time when I was briefly pursuing an ill-advised career as an ecclesiastical historian specialising in the 15th Century, I went one summer to research in its library.
A priestly custodian judged that my frock -- which did not quite reach my knees -- was too short and turned me away.
Since travellers from the UK were allowed only a £50 travel allowance, and I had been warned to spend some of it on a good dinner for a priest who might help me get the records I wanted, I couldn't afford to buy clothes.
At a time of short skirts, I had only one that met requirements. It was woollen, there was no air-conditioning and I sweltered all week.
I had already taken against the Vatican at school when the religious instruction nun failed to give me a satisfactory explanation as to why, if she was right that God ensured that the best person available became pope, such a huge majority of them were Italian (today's figure is Italians 175: Rest of World 90).
The conclusion I reached in my late teens was that the church's nerve centre was run by a crowd of old women. This was unfair to old women, most of whom are in touch with reality and not obsessed with power.
I would learn gradually that all institutions are dominated primarily by an instinct for self-preservation.
Yet the Vatican is an extreme example.
It governs almost 1.2 billion people worldwide, yet it is run by a tiny unrepresentative cabal who have so doggedly rejected any kind of reform that they imperil its very existence.
Moral cowardice and cover-ups led to the scandal of child abuse. Now leaks of confidential documents are exposing the turf wars.
By the Vatican I don't mean the city state, but the Holy See -- a sovereign entity in international law.
Pope Benedict governs through the Roman Curia, a complicated structure that includes the secretariat of state, nine congregations, three tribunals, 12 pontifical councils and three offices.
Italians hold 46.4 per cent of the top 28 leadership jobs and 40.7 per cent of the
positions just below.
In theory, the retirement age for all but the pope is 75, so quite a few important posts are up for grabs.
But since the pope is visibly ailing, there's much speculation about his job too. His successor will be appointed by the 404 under-80s in the 492-strong College of Cardinals.
The Italians don't do so well here: they have 10.4 per cent but only 7.2 per cent with voting rights.
The secretary of state -- the prime minister in this bureaucracy -- is Cardinal Tarcisio Bertone (Italian, 77).
An authoritarian who allegedly prefers politicking to management, he has more than once landed the pope in PR disasters.
No one told Benedict the well-known facts that the man he appointed to be Archbishop of Warsaw had been a police spy or that the four rebel bishops he rehabilitated included a Holocaust-denier.
Last year, Bertone notably saw off Archbishop Carlo Maria Vigano, who as secretary general of the Governatorate of the Vatican city state, had reportedly turned a $9.5m deficit into a $40m surplus, but whose reforming zeal had won him few friends.
Instead of being given the top job when his boss died, he was shunted off to be apostolic nuncio in Washington.
Bertone won that one, but hubris may be his downfall.
What enraged his enemies was the announcement last January of the list of 22 new cardinals: of 18 under-80s, 10 were Vatican insiders, of whom seven were Italians.
The retaliation began with the leaking in January of letters from Vigano to the pope in which he had warned that his transfer would "provoke confusion among all those who've believed that it's possible to clean up so many situations of corruption and dishonesty".
These have been followed by a raft of documents that exposed power struggles inside the Vatican.
They are damaging to Bertone and include intensely embarrassing revelations about corruption in the Vatican's central bank, aka the Institute for the Works of Religion.
True to form, the Vatican is hunting the Vatileakers rather than addressing the revelations: the pope's butler is now in the custody of the Vatican police but is regarded as no more than a 'delivery boy' for enemies of Bertone and Monsignor Georg Ganswein ('Gorgeous George'), the pope's private secretary.
The Italian press is in a frenzy and the pope is begging for calm.
The Holy See is an absolute monarchy run by squabbling old, male, celibate courtiers dominated by one nationality.
It is a self-evidently absurd anachronism.
Even loyal Catholics now believe it has little to do with faith or justice.
Unless the next pope is a moral giant with a clear vision, the whole rotten edifice may just crumble into dust.