The new complexes [NEt₃H][M(HL)(cod)] (M = Rh 1 or Ir 2; H₃L = 2,6-dioxo-1,2,3,6-tetrahydropyrimidine-4-carboxylic acid, orotic acid; cod = cycloocta-1,5-diene) have been prepared by the reaction between [M₂Cl₂(cod)₂] and orotic acid in dichloromethane in the presence of Ag₂O and NEt₃. They crystallise as dichloromethane adducts 1·CH₂Cl₂ and 2·CH₂Cl₂ from dichloromethane–hexane solutions. These isomorphous structures contain doubly hydrogen-bonded dimers, with additional hydrogen bonding to NEt₃H⁺ cations and bridging CH₂Cl₂ molecules to form tapes. The use of NBuⁿ₄OH instead of NEt₃ gave the related complex [NBuⁿ₄][Rh(HL)(cod)] 1′ which has an innocent cation not capable of forming strong hydrogen bonds and in contrast to 1 exists as discrete doubly hydrogen-bonded dimers. Complex 1′ cocrystallises with 2,6-diaminopyridine (dap) via complementary triple hydrogen bonds to give [NBuⁿ₄][Rh(HL)(cod)]·dap·CH₂Cl₂ 3. Complex 3 exhibits an extended sheet structure of associated [2 + 2] units, with layers of NBuⁿ₄ cations separating the sheets. These structural data together with those reported previously for platinum orotate complexes suggest that the steric requirements of the other ligands co-ordinated to the metal are important in influencing their hydrogen-bonding abilities. The solvent of crystallisation, the hydrogen-bonding propensity of the coligand and the nature of the counter ion also determine the type of association in the solid state.