The ground-state rotational spectrum of (AlI)-Al-27-I-127 has been investigated by Fourier-transform microwave spectroscopy. AlI was generated by reaction of laser-ablated aluminium vapour with methyl iodide. The rotational constant (B-0), nuclear quadrupole coupling) and the nuclear spin-rotation constant of iodine (Cl) have been re-determined with high precision. The nuclear constants (chi(Al)(aa:)chi(I)(aa)) and the nuclear spin-rotation constant of iodine (C-hh(I)) have been re-determined with high precision. The nuclear spin-rotation constant of aluminium (C-hh(AI)), the nuclear spin-spin constants (D-aa(Al.I),delta(Al.I)) and the dependence of the coupling constant Z(aa)(I) on J (chi(I)(J)) were determined D-aa(Al.I) and delta(Al.I) agree with calculated values and chi(I)(J) is consistent in sign and magnitude with the known dependence of chi aaI on vibrational state. (c) 2006 Elsevier B.V. All rights reserved.