Let K be a knot in an integral homology 3-sphere I pound with exterior E (K) , and let B (2) denote the two-fold branched cover of I pound branched along K. We construct a map I broken vertical bar from the slice of trace-free -characters of pi (1)(E (K) ) to the -character variety of pi (1)(B (2)). When this map is surjective, it describes the slice as the two-fold branched cover over the -character variety of B (2) with branched locus given by the abelian characters, whose preimage is precisely the set of metabelian characters. We show that each metabelian character can be represented as the character of a binary dihedral representation of pi (1)(E (K) ). The map I broken vertical bar is shown to be surjective for all 2-bridge knots and all pretzel knots of type (p, q, r). An extension of this framework to n-fold branched covers is also described.