2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/117872We 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.20 pages, 14 figures; Minor expositional improvements, typos corrected throughout (most seriously, the x,y coordinates used in discussion of intersection points beginning page 13 of previous version were incorrectly--but consistently--flipped)Geometric Topology57R58; 57M12; 57M27text