HMB..I couldn't disagree more.
The FIRST bird is the key to good scores in doubles - and you said it yourself when you typed "for most shooters it(the second bird) has stopped rising or is falling".
I agree with you...for most doubles shooters the second bird HAS stopped rising or is falling, and this is the root of the problem. The first bird has to be taken quickly...almost a spot shot. Very little barrel movement. So that you can get to the second before it peaks.
That comes from a refinement of your hold point, so that you can take that first bird quick enough to give you time to get to the second bird while it's still on its way up.
Too low a holdpoint, you have to chase the first bird - making you slow to the second, so now it's falling while you're trying to hit it.
Too high a holdpoint, you have to wait too long for the first bird to rise to where you're waiting for it...making you slow to the second bird.
Lastly...you should miss about half first birds and half second birds in a round (I said 'about'). If you get all 25 first birds, I know without looking at you that you're taking too long to shoot it. Spot it, smoke it, and move on. Don't admire the break...get to the second target.
Give me an hour and six boxes of shells and I believe I can have any decent singles shooter breaking over 40 per round on doubles.