  Using the relation between Khovanov homology and the Heegaard Floer homology
of branched double covers, we show how Khovanov homology can be used to
establish tightness of branched double covers of certain transverse knots. We
give examples of several infinite families of knots whose branched covers are
tight for Khovanov-homological reasons, and show that some of these branched
covers are not Stein fillable.
