Well I trimmed a couple of figs this summer and decided to put the cuttings with a few small or cut leaves left into potting soil and see what happened.  Well, they are pretty much fully rooted in quart containers by now!  I believe that the key was to hide almost the entire cutting into potting soil and barely allow the leaves to be seen.  I watered sparingly and kept them in the shade, then gradually exposed them to full sunlight.

I would recommend experimenting with this next summer if you are planning on trimming your trees while they are actively growing.  I'm sure these trees will take off a lot faster next growing season now that they have a head start on winter dormant cuttings!