X-ray diffraction and diamond anvil techniques were used to measure the isothermal compressibility of K(3)C(60) and Rb(3)C(60), the superconducting, binary alkali-metal intercalation compounds of solid buckminsterfullerene. These results, combined with the pressure dependence of the superconducting onset temperature T(c) measured by other groups, establish a universal first-order relation between T(c) and the lattice parameter a over a broad range, between 13.9 and 14.5 angstroms. A small secondorder intercalate-specific effect was observed that appears to rule out the participation of intercalate-fullerene optic modes in the pairing interaction.