I used my 19 inch carryon and a laptop bag (and spent at least an hour trying to make everything fit that woulda fit had I used the backpack. No can do.
In the end, I packed my purse in checked and put the necessities on my person/in the laptop bag (passport, etc etc). I bought a Scottevest which helped a lot. Not enough to avoid checking something I didn't want to check, but still...
I am here, now, to get home Saturday with the same luck.