Ac loss due to coupling currents in a Rutherford cable can be controlled by increasing the interstrand contact resistance through adjusting the level of native oxidation of the strand, coating it, or by inserting a ribbon-like core into the cable itself. In an investigation of coupling loss, magnetic and calorimetric measurements were performed on: (i) a 'reference pair' of bare and stabrite-coated uncored Rutherford cables; (ii) a series of stabrite-coated cables with cores of titanium, stainless steel, and kapton ribbon; and (iii) a series of bare-Cu cables with fixed overall thickness but with cores of successively increasing thickness. Measurements were made both with and without the release of uniaxial pressure between 'curing' and measurement and, in the former case, after reapplication of in-cryostat ('cold') pressure. The total ac loss was measured as a function of the ramp rate of a magnetic field applied in either the face-on (FO, perpendicular to the cable's broad face) or edge-on (EO) orientations. From the coupling-current loss components, standard formulae enabled the interstrand contact resistances R ⊥ (crossover) and R (side-by-side) to be determined. These were combined, for the purpose of discussion, into an effective FO-measured contact resistance, R ⊥,eff (R ⊥ , R ). It was noted that under the pressure-release measurement condition: (i) although the inclusion of a core (of any of the three materials) generally brings about a strong suppression of the FO loss, its presence at fixed cable outer dimensions causes an increase in the EO loss presumably as a result of increased side-by-side contact; (ii) increases in the core thickness, again at fixed cable size, resulted in still further increases in the side-by-side contact, and concurrent small reductions in the existing large R ⊥,eff (R ⊥ , R ). Although previously reported results had confirmed that the insertion of a core into a stabrite cable removed the cold-pressure sensitivity of its R ⊥,eff -a highly desirable outcome-it was noted that the cored-enhanced R ⊥,eff s were then much larger than the 20 or so µ called for by dipole magnet designers. With a view to correcting this problem a series of cables with reduced-width cores was proposed for future fabrication and measurement.