In reply to simonfilson:
There are hundreds of slab climbs in Kalymnos in the lower grades but if you want testing ones at 6b and above try these locations:
Poets has several great sustained slabs on its right hand side, O Brothers 6b+; Alcman 6c; and Solomos 6c+ are good examples.
Boomerang 6c+ and Mecki Messer 7a+ on Panorama fit the bill well and are particularly memorable, the former for its 3 distinct and different cruxes and the later for its sustained and subtle sidesteps.
Kalydna has steep slab and wall climbs of a completely different character but its best examples at the slabby end of the spectrum are Theodora 6c+; Tassir 7a: and Sickle 7a+.
On Stankill there is Gunpowder Plot and its extension which gives 40 metres of superb and sustained grey-slab climbing of the highest quality which would be a complete anathema to the burly jug-jockeys swinging around on the tufas in the Grande Grotte. I thought it probably the most satisfying lead of my trip last May. But its 6c guidebook grade is on the rather mean side; think 6c+/7a but do it in one pitch for maximum enjoyment.
If any of you think that slabs on Kaly are all the same then try ET for a bit of a change. This is the nearest thing on Kaly to a bolted High Tor in Derbyshire. Very English style white limestone with several superb but toughly graded 6s from Claude Idoux. Try the innocuously named Lily and Rose both allegedly 6b but amongst the best (and probably hardest!) of that style and grade on the islands.
Back on Spartan Walls thanks very much to Carl for his endorsement of my route Leonides which certainly needs slab climbing credentials for the exit moves left from the top of the yellow groove. However, another and only slightly harder route hereabouts is Yanap 7b+ which involves several superb slabby sections and is a massive 50metres long. Can you keep concentrating that long?