The hilltop hideouts, with their spartan cells, are seldom full out of peak season; even during the summer months, when coastal hotels are overbooked, they continue at their leisurely pace and have cool rooms on offer at good prices.
And you don't have to become a monk to enjoy them - only one of the monasteries offering lodging is, in fact, still run by a religious order (Lluc Monastery).
It is the stress that the mass tourist industry has brought to much of the island that has driven some young locals back to these ancient sites, which they look after as lay caretakers. These people can always tell you stories about the history of their monasteries. If you want a meditational atmosphere, you will find it here. You might be offered a yoga class by a caretaker who has spent time in India. You could even find yourself becoming part of a local pilgrimage to the hills.
The monasteries are not all the same. The most sophisticated, at Lluc (in a valley in the northern mountains), contains a community of friars who look after the buildings, maintain the church, and run a boarding school. At weekends the place gets busy, and the three or four restaurants outside the monastery are packed. Lluc is the most important site of pilgrimage on Majorca, and happens to be home to the patron saint of the island - the Mare de Deu de Lluc, the Virgin Mary- a figure of which is kept in the church. As well as being the most religious of the monasteries on Majorca, it is also the most expensive, costing pounds 10 per night for a single room, although a room for six only costs the equivalent of pounds 20.
A more austere atmosphere prevails at the Puig de Santa Maria, an hour's walk along a narrow road from Pollensa and the only monastery which cannot be reached by car. Provisions for the monastery at the top are taken up by mule. The hour's walk takes you to ever more spectacular views of the Tramuntana mountains and the Formentor peninsula.
Running the monastery are a young couple from town, Antoni Pons and Cati Coll. Their main problem is trying to convince visitors that life on the top of a mountain requires caution in the use of water.
The Puig de Santa Maria has simple cells on the second floor, and bathrooms in the corridor. You ask to have the hot water put on. Cati cooks Majorcan food, such as the vegetable and bread stew known as sopes, as well as paellas for 1,000 pesetas per head (a little under pounds 5). Rooms are likewise under a fiver a night. Monastic peace comes cheap round here.
Another monastery, on the east coast of the island, is Sant Salvador, overlooking the town of Felanitx. The ageing monks of the Orders of Sant Pau and Sant Antoni lived here until 1992, when they finally moved to more comfortable lodgings. Now Sant Salvador is looked after by a family from Felanitx - the donats, as all such caretakers are known here.
The donats run the cells and the souvenir shop, and the kitchen which contains a small gas ring for lodgers. Another local family runs the quiet restaurant, which is in the vaulted east wing.
At weekends, locals come here to eat what they consider to be the best paella in the world. The decor of the entrance hall is an odd mixture of religious art and cycling mementoes, the latter mostly offerings made by the world cycling champion from Felanitx, Guillem Timoner, to the local Virgin.
Across the plateau of the interior of Majorca, the characteristic shape of Randa, the highest mountain near the centre of the island, is visible. There are three monasteries at Randa. It is associated with one of the most famous Majorcans from medieval times, Ramon Llull, philosopher and preacher, who started a crusade to convert the infidels of north Africa to Christianity in a cave on the top, now somewhere under the foundations of the Nostra Senyora de Cura Monastery.
The other two monasteries on the mountain do not have lodgings open to the general public, but can be visited. The third monastery here, Sant Honorat, is still used as a religious centre.
And the Mediterranean? You won't miss it. A tour of the monasteries of the island is a fine way of seeing the Med - which gleams down below - without feeling remotely like a package tourist.
EasyJet (tel: 0870 6000 000) fly London-Luton to Palma de Mallorca from pounds 88 return, including tax. These fares tend to go months in advance, so book early. Virgin Sun (tel: 01293 432 100) have fares to Palma from pounds 99 return, including tax.
Travelling between monasteries: there are no public transport links, except in the case of Lluc, which can be reached by bus from Inca, which is connected to the capital of the island, Palma, by train. Other monasteries are reached by car or bicycle, which can readily be rented in coastal areas of the island.
Booking is best done by telephone. It is advisable to book lodgings over a week in advance especially in the case of groups. Payment is made at each monastery on arrival.
Lluc (tel: 00 34 971 517 025). Access: road from Inca, Sller, or Pollensa; price: 2,500 pesetas (just under pounds 10) for a single room, 3,500pta per double room, 4,700pta per room for six people sharing.
Puig de Maria, Pollensa (tel: 00 34 971 184 132). Access: from Pollensa; walkers/mountain bikes only; price: 1,000pta per head per night.
Sant Salvador, Felanitx (tel: 00 34 971 827 282). Access: road from Felanitx; price: 750pta per head per night.
Cura, Randa (tel: 00 34 971 660 994). Access: road from Algaida; price: 1,000pta per head per night.