Doing a three-way compare with Git and KDiff3

Is it possible to set Git up so that I can use the three-way compare in KDiff3?

I have two branches that are far too different to auto-merge them, I simply have to check each merge point and I think the best way would be to check out the branch I want the changes from the other branch and say

git difftool HEAD_OF_OTHER_BRANCH -- .

And then select Merge File in KDiff3. After having gone through the files I'd just commit.

I have set up merge.conflictstyle and diff.conflictstyle to diff3 but KDiff3 still starts with a two-way diff. Is this possible? I guess if Git also sends the common ancestor's hash as a parameter, this is possible, but does it?

There is discussion about how to do this with SVN and BC3, but I couldn't find anything for Git and KDiff3.