  Let $K$ be the field of fractions of a local Henselian DVR with perfect
residue field. Assuming potential semi-stable reduction, we show that an
unramified Galois-action on second $\ell$-adic cohomology of a K3 surface over
$K$ implies that the surface has good reduction after a finite and unramified
extension. We give examples where this unramified extension is really needed.
Moreover, we give applications to good reduction after tame extensions and
Kuga-Satake Abelian varieties. On our way, we settle existence and termination
of certain semi-stable flops in mixed characteristic, and study group actions
and their quotients on models of varieties.
