In reply to Rapsling:
I found Mulhacen to be more of a walkers peak outside of the winter. The rock appeared unsuitable for climbing kind of shale like and crumbly, I don't think there are big faces requiring multi day ascents and hauling. Just a pair of trainers to hike up and down from the village.
I might of missed something however and there could well be somewhere. It was seriously hot when I was there during June a few summers ago, I found some climbing close by in Orgiva but it was grubby, didn't see much traffic and difficult to locate.
I can seriously recommend the Picos however an amazing place, was truely astonished by the amount of climbing and the size of some of the walls. Particulary recommend Naranja its sporty trad in places and a long day out including walk in!
Quite away from the south though!