I closed my eyes and counted to 10. When I opened them the aeroplane's information screen was still glaring at me. It bore the disquieting information that I was flying over London at 30,000ft. Momentarily, I was only six miles from home, but the Boeing 747 that had been my residence for most of the previous 24 hours was flying on for another 40 minutes, and then I would be 200 miles further away and even more tired. There was nothing magical about this mystery tour.

Initially, the day trip to hell and back seemed one of the great air bargains of all time. This summer, the Dutch airline KLM launched mystery day trips to the United States. You pay the airline pounds 127, and it flies you across the Atlantic and back. You choose the day, but KLM selects the flight. Your destination could be anywhere in the eastern part of the US, such as Atlanta, Chicago or New York. Or it could be Houston. But not without a catch or two.

The first is that the flight leaves from the Netherlands, which immediately tips the cost the wrong side of pounds 200. Getting to Schiphol airport by the appointed hour of 8am makes you feel dull and hazy. As far as I could tell, I was the only one who had rolled up for the mystery tour that day. At the ticket desk, the staff made no attempt at theatricality; no sense of opening an envelope to reveal that the winner is . . . Houston] They merely hand you the ticket, plus an official letter to wave at all and sundry, and bid you farewell with a 'poor dear, does he know what he's let himself in for?' expression.

The letter is hardly designed to enhance your self-esteem. 'This person,' it explains in less-than-perfect English, 'is an unexperienced traveller.' Your interest, it continues, is to learn about transatlantic air travel.

For anyone who has been on an aeroplane before, the learning curve is not steep. You sit there and eat the (passable) food that is put in front of you. You have little choice but to watch the movies which flash past on the uncomfortably close screen. The rest of the time you marvel at the capacity for Heineken demonstrated by a couple of passengers determined to drain the Dutch beer lake.

After what feels like (and nearly is) half a day, you touch down at Houston. At US airports, all arriving passengers, however 'unexperienced', have to clear immigration even if they are continuing straight out, or back, on another flight.

'Point of origin?' the immigration form demanded. Easy: Amsterdam.

'Purpose of visit?' A bit trickier. Fortunately, the letter which was my laissez-passer told me exactly what to write: transit.

'Destination?' See answer to question one, above.

The official who studied these replies had another query. 'You crazy?' he muttered as his rubber stamp thudded on to my passport. I had come to the US for precisely three hours, but he allowed me a stay of six months. I wondered if he knew something I did not about KLM's timekeeping.

Houston Intercontinental Airport was wasted on me. People who appreciate these things voted it second-best airport for business travellers last year (Amsterdam came first), but it looked like a wantonly vast warren of glass and steel to me. I had been on US soil for half an hour already, and wanted to see the country before any more of my 180 minutes expired.

The right taxi driver, imbued with a sufficient sense of haste, could cover the 25 miles to downtown Houston in 27 minutes. But not knowing which US city you are going to means you cannot pre-plan and, maddeningly, many minutes were spent convincing the tourist office staff that I needed to see Houston in (by now) less time than it took Holland to beat Ireland in the World Cup.

We devised a stroll which took me from parking lot to shopping mall via deserted downtown streets (although it was lunchtime) and premises protected by heavily armed security guards. If this was all you saw of the US, you would want to be on the next plane out, too.

On board again, I was now able to demonstrate an impressive familiarity with the plane's layout and even helped repair the recalcitrant tray table I saw someone battling with on the way over. Jet lag never had a chance to set in, but fatigue certainly did. Impeded by headwinds, we were still over London when I should have been changing planes at Schiphol.

Sleepily trying to count blessings, the best I could do was to calculate that with the frequent-flyer miles earned between Amsterdam and Houston, I needed to make the trip only twice more before I got a free flight on KLM - to a place of my choosing.

The Dagvlugje ('day flight') from Amsterdam should be pre-booked with KLM in Amsterdam, on 010 31 20 474 7747. The fare of approx pounds 130 must be paid by cash or cheque, not credit card. KLM also offers mystery day trips within Europe for approx pounds 58. Return flights between London and Amsterdam cost under pounds 80 with KLM, Air UK, British Airways, British Midland or Transavia.

(Photograph omitted)