I was lucky enough to have received some cuttings from an heirloom fig tree, planted in Raleigh over 30 years ago.  The owners weren't sure of the variety, but thought it might be a Brown Turkey (very common in NC).  I'll have to go back and get pictures of the entire tree, it's easily 20-25 feet high.  I haven't eaten enough good figs to have developed a palate yet, but they had a berryish taste with a little crunch.
The 5-lobed leaves resemble those on figs4fun.com/Thumbnail_Brown_Turkey.html, but most branches have 1-, 3- and 5-lobed leaves on them.
       

Looks like my celeste figs.

That's a celeste

Thanks for the help!  The more experience I get with growing, the better I'll get at identifying them :-)

I had thought about trying out the method here http://figs4funforum.websitetoolbox.com/post/rooting-summer-cuttings-201-5451326?highlight=summer+cuttings&trail=50 but became dismayed that it turned into a prayer-fest, and not all the instructions were listed :-(
Has anyone tried this method?  I had not read anything about cutting the leaves off where they connect to the stem, but the reasoning behind it seems sound.