I for some reason didn't see this picture before. In this picture, the leaves are draw before the tree trunk... which means the tree trunk must be in the transparent bucket if the leaves are in the transparent bucket.
If moving the leaves to the opaque bucket fixes this then it's just a matter of luck, I guess.
Is each leaf a separate object? If not then they will always self-occlude.
Actually, if you put them in the opaque bucket then it might look like they are working better but only because the background will be black when they are drawn. The sky is drawn after the opaque bucket. Put the leaves back in the transparent bucket and then remove the sky... I bet they will look "fine" then, too.
And if you are ok with the effect then you can fix it in the texture (or hack the shader) to not have any partial transparent pixels. Basically, if a < 1 and a > 0 then mix the color with black and set alpha to 1. I could explain how I'd do it in photoshop.