The synthesis, structure, and magnetic behavior of the complexes Cu(qnx)Br-2 (1), Cu(2,3-dmpz)Br-2 (2), Cu(qnx)Cl-2 (3), and Cu(2,3-dmpz)Cl-2 (4) (qnx = quinoxaline, dmpz = dimethylpyrazine) are described. Both X-ray structural data and fitting of the magnetic data suggest that the compounds are well-described as strong-rung, two-leg magnetic ladders with J(rung) ranging from -30 K to -37 K, and J(rail) ranging from -14 K to -24 K. An unexpected decrease in the exchange constant for J(rail) (through the diazine ligand) is observed when the halide ion is changed from bromide to chloride, along with a small decrease in the magnetic exchange through the halide ion. Theoretical calculations on 2 and 4 via a first-principles bottom-up approach confirmed the description of the complexes as two-leg magnetic ladders. Furthermore, the calculations provide an explanation for the experimentally observed change in the value of the magnetic exchange through the dmpz ligand when the halide ion is changed from bromide to chloride, and for the very small change observed in the exchange through the different halide ions themselves via a combination of changes in geometry, bond lengths, and anion volume.