There's just one drawback to staying in a romantic old windmill on a remote Greek island. You guessed it - the wind. We tend to forget that those picture-postcard white towers were put where they'd catch the best of the breeze.

And though the Doctor's Windmill, on Kimolos, is now sans sails and has been turned into holiday apartments, climate change wasn't part of the conversion. When the wind blows here, you know about it.

But the windmill's pluses are many: you have an almost-all-the-island view from your terrace; you can never get lost because you can see it from miles away; and you do feel quite privileged to stay there.

Particularly because the Doctor's Windmill was home for more than 50 years to Dr Stelios Logothetis. He treated patients not only here on Kimolos but on the neighbouring islands of Milos, Folegandros and Sifnos.

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When he died at the age of 99, his grand-daughter Anna was six - now she is the young woman in charge of the windmill and its five apartments.

The wind pinned us down for a few days in this southwest corner of the island, leaving us running after errant hats and struggling to walk around without cups of tea levitating from trays. But the large, sandy beaches of Aliki, Bonatsa and Kalamitsi remained sheltered as well as shaded, providing relief from this early mini-meltemi in mid-July.

And when the wind dropped, we were able to discover the idylls of the island: from the cool and labyrinthine alleys of the chora (main hilltop village) to the dramatic sun-cooked mountainsides, over which we hiked to the secluded beaches of Monastiriya and Soufi in the north.

Although it was high summer, there were few tourists here. Even Greeks, said Anna, can look puzzled when you mention Kimolos (and UK visitors are almost unknown). Only when you mention its bigger sister island of Milos do people get an idea of where it is.

Nights on Kimolos were still and beautiful beneath a star-filled, unpolluted sky. We would sit either in a quiet taverna on the beach, a couple of feet from the water and the moored fishing boats, or at the restaurant in the chora's central square, where local children played the old-fashioned way - swings, roundabouts and football - a chaotic melee of joy.

At the other end of the chain of the western Cyclades is the island of Kythnos. Ferry-wise, it is four or five hours north of Kimolos and just three hours from Athens - yet a world away from the capital's intense buzz and oven-like heat.

It's ringed with at least 20 beaches, almost all of them excellent and some of them sublime. In less than an hour's hike from the little port of Merihas - with its bars, tavernas and tat-filled tourist shops - we swam and sunbathed all day on a perfect beach that we had totally to ourselves. And the water here was so clear that it seemed unreal, even in this island of wonderful swimming places.

On Kythnos, we stayed just outside Merihas, at Villa Elena - quite different from the Doctor's Windmill but equally romantic. At the top of the steep cliff above the small bay of Martinakiya, it was reached by a precipitous stairway - at night illuminated by little lights that gave it the look of an enchanted citadel.

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