"spider-legs" is what I term "collapsed hand." There are many [famous] pianists that play this way. I guess that's why I'm not famous.

Paradise comes only after much tedium. Once you know what you want to accomplish (in this case, finger curvature and eliminating unnecessary tension) the magic is probably not in the exact exercises, but in how long you spend on them. For me, it was half a year of 100% exercises, no repertoire, just exercises every single day. OK, it was half a school year, so 4 months and not 6. But still. I felt so foolish at a fancy conservatory playing only simple exercises for so long. However, I believe my teacher was exactly right to require this. The "instinctive" actions got retrained in that time, so when I did go back to playing repertoire, I distinctly felt that my hands could operate in two very different ways, and when I noticed the less productive way creeping in (usually by means of that dull ache that starts up in an old injury) I could stop and switch to the more productive way.

Anyway, some of the exercises I was taught:
-Make the bridge shape with fingers 2-3-4 on F#-G#-A#, 1 and 5 on B and F at first, hands separately at first. Before starting, make the bridge shape and confirm that there is no unnecessary tension. Play finger 1 by pressing down only finger 1. Confirm that no other fingers lift. Return to the tension-free bridge shape. Then play finger 2. Continue to finger 5 and then reverse course to finger 1. When this can be successfully done, move 1 and 5 to C and E and repeat the exercise.
-Scales in quarter notes followed by quarter rests at quarter note = 80 or slower. Hands separately at first. Use the rest to return to the tension-free bridge shape.
-Scales in sixths (1 and 5 on the same hand make a sixth) in quarter notes followed by quarter rests at quarter note = 60 or slower. Strike the key from the air, play only by pressing down and maybe squeezing the hand a little, make a bridge-shaped curve when playing. On the rest, contract hand into a completely relaxed droopy position in the air like a crumpled-up tissue. Do this sometimes using the wrist to raise and lower the hand, sometimes using the arm. Eventually, do this with two hands at the same time, playing the scales in contrary motion.
-Scales in sixths as above but add a third note in each hand, playing fingers 1-2-5 (1 and 2 are a third apart).

Eddy:

http://www.youtube.com/watch?v=n5SjyikVztQ
Helene Grimaud with "dead spider" hands as we say in my studio. Do we care that she uses this hand position? No, no we do not. At least, provided she can play this way for many years to come and does not deprive us of music by suffering an injury. May it never happen.

Alright, I'll see what I can do with them in the near future, after my current piano-playing commitments are done. Thanks again for all the exercises and stuff. Perhaps I might even get a good teacher to supplement this.

I had a teacher "redo" my technique (successfully, thank heaven) when I was 22. One of the exercises that we used was the first one explained by Heather - the one with 2-3-4 on F#-G#-A#. Instead of F and B for 1 and 5 we used E and C, which I found to be a little more relaxed. It might depend on the size of your hands.

We would then move to the following (with the fingers still on these same keys): hold the E down with the thumb, and play 2-3-4-5-2, then 3-4-5-2-3, etc., also reversing directions. (With similar but mirror-image exercise in the left hand).

We would then move up to trills with all the different combinations of fingers (and the hands still in this same position), with only the trilled fingers moving. The trills should be practiced in both directions.

There were other exercises as well, but I don't remember many of them. I do remember an exercise which emphasized focusing the eyes on the target key when leaping. My teacher was fond of saying "It's difficult to miss a key when you're looking right at it."

I like the sound of that, but is there not another school of thought which discourages watching your fingers? By depriving the fingers of ocular support you force them to stand on their own feet, so to speak, and to find their own way in the world, by magic or a special kind of muscle memory by which they judge the leap distance by themselves.

The eyes can't always help, because they can't simultaneously "focus" on two different leap targets which are very far apart, for example in Leyenda, where the hands have to leap large distances in opposite directions at the same time. The best the eyes could do is guide one hand; the other hand still has to look after itself.

@rainer: Oh and yes, I meant 'playing by the nails literally'. You're right in the hand has to exert more strength to keep the finger in place, though, something I totally forgot about. Ironically my teacher would always ask me to cut my fingernails if they were too long because of the clitter clatter thing. It has not once caused me pain however.

I agree with you entirely.

I agree with rainer on this, because soon enough you'll bump into literature that simply doesn't allow pre-targeting. And in a related fashion but worse, pianists that don't develop the ability to play chords and octaves without "pre-touching" them are at a HUGE disadvantage in demanding literature. Some stuff cannot be played efficiently without the ability to trace through the air to a "direct hit" for the required playing. This skill is learned with graded steps begining with inversions of triads by changing the ratio of time on the key (sound) to switching position (silence, all the time maintaining a strict tempo). I would teach my students not to execute a "false gesture," meaning the hand moves to play ... and then waits... and then plays; the move should result directly in playing.

More interestingly, I have wondered much about the function of the two hemispheres of the brain, together with the dominant handedness that most of us have (one hand or the other, just not ambidextrous), and the inherent bi-handed nature of playing the piano. I noticed, that mostly, I observe one hand and the other seems to play more by its own control. Then I theorized that it could be of a beneficial nature to try to work it the other way, that is to watch the "automatic hand" and force the observed hand to play "by itself." This is really kind of cool (IMO) and likely important from a training/neurologic perspective but I don't have the time to pursue it in a systematic and scientific manner. But I would ask you to try the following: Play some two-handed scales in parallel (or better contrary) fashion and observe how differently it feels depending on which hand you watch like a hawk, and which is left to its own devices. Or try a short piece that you play well already and play it twice, each time watching one hand while ignoring the other, then switch assignments. You will soon discover which way you observe your hands; then spend time working it the oposite way. Let me know what you experience. [I have never heard this notion discussed or published so it is likely original. If you know otherwise, please provide some source reference.]

Actually, if the goal is to open up the hand from a too-closed position, E and C is probably better.

I've long been aware that I play two-handed broken chord and arpeggio exercises much better when I watch my left thumb. No idea why.