Thanks for your replies, but how did you manage to curtail the 'bad habits' that you had before adopting this 'open natural curve' technique? If you were to elucidate what simple relaxation exercises you have done while adopting this technique in brief, it would be definitely worth a shot, because from your descriptions this state sounds reminiscent of paradise. Instinctively my fingers tense up while playing passages (especially the fifth) and doing simple things like turning my thumb over or using my third finger rapidly (e.g trills, tremolos, etc., eventually flailing and causing very irritating mistakes.
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).