A more compressed video format that supports alpha than ProRes 4444?

I need to export clips from AE with alpha.

Quicktime ProRes 4444 works fine, except it creates a huge file.

If I didn't need the alpha, h.264 high quality 1080p HD works well enough.

Is there a way to export alpha with a file size and image quality comparable to the above h.264 format?

And without running AE twice?