Run-flat tyres were the car companies’ way of making more luggage space and cutting cost from each car. But they had their problems including the noise you’ve mentioned as well as a lack of ride quality. Although, to be fair, the latter has improved massively in recent years with new generation run-flats hitting the market.

A good tyre specialist should be able to advise you on which run-flats are the current favourites in terms of noise and ride, as well as grip and price. But it’s worth mentioning that tyre manufacturers are constantly trying to outdo each other, so the improvements keep coming. The best tyre today might not be the best one in a few months’ time.

The concept of a larger (wider) tyre on the rear of your car is to do with grip and handling. Messing about with this relationship could lead to a less athletic car and there are physical limits on what tyre can be fitted to what rim.

You could make the switch to a non-run-flat tyre and buy a tyre repair kit to keep in the boot. In fact, many owners of earlier cars with run-flat tyres have done just that. You still stand to pick up a little ride comfort by doing so, but nowhere near as much of an improvement as you would have, say, a decade ago.