  We introduce a simple combinatorial method for computing all versions of the
knot Floer homology of the preimage of a two-bridge knot K(p,q) inside its
double-branched cover, -L(p,q). The 4-pointed genus 1 Heegaard diagram we
obtain looks like a twisted version of the toroidal grid diagrams recently
introduced by Manolescu, Ozsvath, and Sarkar. We conclude with a discussion of
how one might obtain nice Heegaard diagrams for cyclic branched covers of more
general knots.
