Only software rendering is available on the Dell XPS 13 9343, and
possibly other recent Broadwell-based laptops. This makes the system
extremely jerky and quite unusable.

I tried to compile and run Linux 4, nothing changed. Nevertheless,
adding the xorg-edgers PPA[1] to sources.list and dist-upgrading fixed
this issue and allowed me to get a DRI2 capable GPU.
[1] https://launchpad.net/~xorg-edgers/+archive/ubuntu/ppa

Actually, I'm not that sure xserver-xorg-video-intel is the actual
responsible for this bug, as several pieces have been update (X, MESA,
etc.) by the PPA. I'll try to nail it down soon.
The following information are taken from a freshly installed and
updated Debian Jessie install.

I could nail down the issue a little. Installing
xserver-xorg-video-intel from experimental (with no need to upgrade
other components of the stack) is enough to fix it and get DRI2
support and full hardware rendering.