In reply to Somerset swede basher:
I fully agree with everything MG said, but here's my list if anyone's interested:
Solo, maybe with a rope for abseils, in a single push from the valley:
- Lagginhorn W ridge
- Weissmies S
- Dirruhorn N
- Zinalrothorn S (didn't summit because of weather)
- Matterhorn NE (didn't summit because I was feeling off, subsequently did it with a buddy from the hut and didn't feel like the rope was helping much until I saw a guy fall 20m on the descent and get held by his mate on a rope before getting helicoptered off)
Solo with a rope for abseils, from hut/bivouac:
- Dent Blanche S (this one felt a little sketchy on the glacier after the hut)
- Combin du Valsorey and Grafeneire W (some crevasses for Grafeneire, Valsorey is just a scramble)
Self-belaying the crux pitches:
- Zinalrothorn Kanzelgrat
- Obergabelhorn S face
Other things I have considered and think would doable are Obergabelhorn W (I descended this), Weisshorn E, Hobarghorn via Dirruhorn, Lenzspitze E, Monch, Eiger (inb4 not 4000m)...
My main criterion is the glacier. I've put my foot through enough snow bridges with and without a rope on, and had friends fall in and be very seriously hurt, not to take any chances any more. Having a good trace tracked in helps, but sometimes this just means you can see where the crevasses are but not how big they really are. But sadly many glaciers in the Alps are now shrunken patches of firn and are getting safer from the perspective of crevasses.