  We introduce the notion of minimal reduction type of an affine Springer
fiber, and use it to define a map from the set of conjugacy classes in the Weyl
group to the set of nilpotent orbits. We show that this map is the same as the
one defined by Lusztig, and that the Kazhdan-Lusztig map is a section of our
map. This settles several conjectures in the literature. For classical groups,
we prove more refined results by introducing and studying the "skeleta" of
affine Springer fibers.
