K(2P)Ø, the two-pore domain potassium background channel that determines cardiac rhythm in Drosophila melanogaster, and its homologues that establish excitable membrane activity in mammals are of unknown structure. K(2P) subunits have two pore domains flanked by transmembrane (TM) spans: TM1-P1-TM2-TM3-P2-TM4. To establish spatial relationships in K(2P)Ø, we identified pairs of sites that display electrostatic compensation. Channels silenced by the addition of a charge in pore loop 1 (P1) or P2 were restored to function by countercharges at specific second sites. A three-dimensional homology model was determined using the crystal structure of K(V)1.2, effects of K(2P)Ø mutations to establish alignment, and compensatory charge-charge pairs. The model was refined and validated by continuum electrostatic free energy calculations and covalent linkage of introduced cysteines. K(2P) channels use two subunits arranged so that the P1 and P2 loops contribute to one pore, identical P loops face each other diagonally across the pore, and the channel complex has bilateral symmetry with a fourfold symmetric selectivity filter.