I noticed that Debian Backports had some updated firmware for video drivers, so I wondered if this might help with my problem, but I just couldn't see the firmware update even though I have backports in my sources list.
To cut a long story short, the instructions page in the link above has the following line to add to sources list:
deb http://http.debian.net/debian jessie-backports mainTo get firmware updates, it should of course be:
deb http://http.debian.net/debian jessie-backports main contrib non-free(Firmware is non-free software.)
I've upgraded firmware as follows:
Removed the following packages: firmware-linuxThe rendering issue doesn't seem to have entirely disappeared, although first impressions are that it is happening less frequently.
Upgraded the following packages: firmware-linux-nonfree (0.43) to 20151207-1~bpo8+1
Installed the following packages: firmware-amd-graphics (20151207-1~bpo8+1) firmware-misc-nonfree (20151207-1~bpo8+1)
Upgraded the following packages: firmware-atheros (0.43) to 20151207-1~bpo8+1