Just suppose the Beatles made another masterpiece album in 1967 but locked it away for 40 years. And now you can listen to it for the first time.

That, if you love Greece, is what it feels like to discover you can explore a whole new version of the Cyclades - as wonderfully unspoilt and exciting as the original Cyclades were in the early 1970s (before they put airports all over the place and the sun-lusting masses flooded in).

But can there really be another Cyclades? Yes, known as the Little Cyclades, these islands lie to the south-east of the major group of islands. Some are tiny, some large, some barely populated, some uninhabited. Most are unsung and all have that wild Cycladic beauty.

Largest of all is Amorgos - 20 miles long and with high mountains running the length of its spine, it resembles a mini-Crete. Apart from its two little ports of Katapola (old-fashioned) and Aegiali (aspiring to be young and trendy) and the lovely mountain-top village of Chora, the place is deserted. It's fantastic for walking, exploring and beach-going.

We stayed at Aghios Pavlos, a coastal spot remarkable for little, apart from a couple of small apartment blocks, your basic taverna, and a thin spur of white pebble beach stretching into the sparkling blue. It has nothing much - and it has almost everything.

The apartment we had there was beautiful, the taverna staff were lovely (they actually gave us a free meal on our last day) and the swimming was irresistible.

The beach at Aghios Pavlos is great, but there's also a regular boat that will ferry you across the narrow channel to the neighbouring small uninhabited island of Nikouria - and its beaches. The boat moors twice, giving you two good beaches to choose from - and, for the more intrepid, there is a third, which can only be reached by climbing over a rocky point. On this one, we found we could have most of the beach to ourselves for most of the day. Utterly idyllic.

Amorgos invites you to walk as well as laze in the sun. After taking the bus from Aghios Pavlos to Aegiali, we climbed tracks up into the sun-bathed hills and walked via the vertiginous little church at Aghia Triada and the ruined hamlet of Stroumbos to the sky-high village of Tholaria. Then we half-walked, half-tumbled down a steep and stony path to the lovely remote bay of Vlichada, where we swam in the wild sea that has contributed an eccentric collection of driftwood and wreckage to the pebbly beach.

Before leaving Amorgos, we accepted its greatest challenge: walking eight miles along its central range of mountaintops. Clouds often visit the summits here and we soon found ourselves inside their cold dampness, while thousands of feet below we could see the sun shining on glistering beaches and the blue Aegean.

After negotiating clouds, winds, ascents, descents, goats, farm dogs, and paths so stony that the word "challenging" would hardly begin to describe them, we returned to the realm of the sun and punishing heat as we descended to Aegiali, its beach and the most welcome sea.

We sailed via the twin islands of Koufonissia to Schinoussa. We had been warned that Schinoussa was a one-donkey island with hardly any mod cons, where nothing ever happened. So how did we find ourselves dancing beneath the stars, along a dark winding lane at 3am, with an electric gypsy violin playing so loudly in the club that we'd just left that you could hear it literally across the whole island?

We nearly didn't pay the 20 euros each to see violinist Nikos Hatzopoulos at Bar Vrachos - outrageous price, we thought for some hick fiddler. But a few moments after Nikos hit the stage at midnight, we realised he was a superstar and that he was worth every cent. "How long will he play for?" I asked the man selling tickets. "Until the morning," he replied.

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