Column background in QTreeView

[Joel Bodenmann]

How can one set the background color of just one specific column in a QTreeView?
I tried using the Qt::BackgroundRole in my model but the result is not satisfying as this only affects the rectangle of the item. Screenshot: http://paste.ugfx.org/sores/7505d64a54e0/a5bf1d94d58d.jpg

What want is that the entire column has a solid background color. Basically the same as QTreeView::setAlternatingRowColors() would fill the entire row with a solid background color.

Any ideas?