On a packed London tube train I was contorting my neck, trying to see through the crowd and check which station we had arrived at.
The experience reminded me of something, but I couldn't put my finger on it.
Then I remembered -- it was visiting the Sistine Chapel and the Raphael rooms in the Vatican Museums.
The same feeling of half-suffocated, frustrated claustrophobia had overwhelmed me a few years ago as I shuffled along with the tide of tourists, waiting for a gap to open so that I could steal a glimpse of Raphael's frescoes, or find an unencumbered vantage point from which to view Michelangelo's ceiling.
When God created Adam, he surely didn't imagine quite so many of his progeny crammed into one place at the same time.
I've suffered too in the Basilica San Marco in Venice, where, much of the time, the press of visitors is so great that the attendants won't let you stop to look properly at the mosaics. Rather like policemen at the scene of an accident, they insist that you keep moving.
There's a similar system in the Tower of London, though here it is automated -- a moving walkway runs past the crown jewels display case to prevent a scrum developing.
A few institutions are attempting to try to deal with the problem of overcrowding, most recently the National Gallery in London, with its announcement that it will be limiting the number of visitors who will be able to enter the Leonardo da Vinci exhibition when it opens in October. And Giotto's Scrovegni chapel in Padua limits entry to 25 people every 15, sometimes 20, minutes.
But it's hard to avoid the feeling that the greater battle is being lost. As tourism grows and tens of millions more first-time visitors fly into Europe from India, China and the Far East with the 'Mona Lisa', 'The Creation of Adam' and St Mark's Square at the top of their wish lists, surely the problem can only get worse?
I have some good news, however. The more creative cultural tour operators and tourist agencies are offering an increasing range of tours that allow you to visit some of the most popular sites out of hours.
Several of the best specialists have offered privileged access for some years and the range and variety of access they offer is increasing.
What I hadn't realised, until I was contacted by a small tourist agency in Rome, was that you don't have to sign up to a package tour lasting several days to beat the crowds.
I joined a private Vatican tour run by Italy With Us (0039 063 972 3051; italywithus.com) one Saturday evening in April.
Rolling up to the great bronze door of the museums an hour or so after closing time, we were admitted to the cavernous ticket hall, which normally swarms with tourists. Our group was nine strong, all Americans, led by our art historian guide and escorted by one of the museum attendants.
While the cleaners dusted and polished around us, we were whisked through the ticket gates and glided up the empty escalators into the heart of the museums. I know the place very well, but I'd never seen it like this before: devoid of people and so quiet, almost melancholy.
With a strict two-hour time limit, this was very much a highlights tour, taking in, for example, the sculptures of Apollo and the Laocoon in the Belvedere Courtyard, the great Roman porphyry bowl from the baths of Caracalla, the gallery of tapestries and so on; but the best was left for the last half-hour of the visit.
Raphael's fresco, 'The School of Athens' is a trompe l'oeil composition -- Plato (portrayed as Leonardo da Vinci) and Socrates are the central personalities among some 40 artists and thinkers from the ancient Greek and Renaissance worlds, who have gathered on the steps of an architectural tableau.
It's a complex scene, which recedes into the distance through a series of Roman arches, and your eye can only truly be deceived if you take it in from the opposite side of the room. Normally, the only way you could do that would be to set off the fire alarm and hang back as the room emptied.
After hours, I had the entire room to myself.
The feeling in a deserted Sistine Chapel is slightly different. Obviously, the frescoes are always visible no matter how crowded it becomes, but, compared with the usual whispering tide of tourists, there is a calm which entirely changes the mood.
As a result, you relax and start to look at the paintings in a different way. Staring up, with no distractions, I noticed, for example, that the central panel is not the celebrated 'Creation of Adam' but the 'Creation of Eve'.
But before I had time to work out the significance of that, our time was up. I lagged reluctantly behind the group, and for just a minute or two I was alone with Michelangelo. Not many people can say that.
The bottom line
So that's the upside; what about the downside? Not quite as bad as you might think. For the tour I did, a single ticket costs €275, and even though that includes the normal entry ticket of €15, you are effectively paying a premium of about €240 a head for the privilege of peace and quiet.
But there is a much more affordable alternative. Italy With Us also offers a 'VIP' tour which gains admission to the museums at 8am, an hour before the normal opening time.
This means you can visit the Sistine Chapel first, before the hordes descend. The two-hour guided tour with a group of about 20 costs €50 a head.
Italy With Us also offers a private 8am tour of the Vatican Museums at €350 for two, which also includes St Peter's Basilica. And in Venice it offers a two-hour visit to the Doge's Palace after it has closed to the public, for €150 per person (group of 10 or more). It can also arrange a private visit to St Mark's Basilica.
The price depends on the number of visitors, but is less than that charged for the Doge's Palace tour.