The rotational spectra of three isotopomers of the complex dimethyl ether-Xe (Xe-132, Xe-129, Xe-131) have been measured by molecular beam Fourier transform microwave spectroscopy. An evenly spaced doubling of ca. 0.2 MHz, due to the internal rotation of the dimethyl ether subunit in the complex, has been observed for the mu(c)-type transitions. The corresponding vibrational spacing, Delta(01), has been determined to be 105(1) and 106(1) kHz for the Xe-132 and Xe-129 species, respectively. This datum has been useful to size the tunnelling barrier of Xe from above to below the COC plane. The nuclear quadrupole coupling constants of the Xe-131 (I = 3/2) species have been precisely determined, chi(aa) = 4.57(3), chi(bb) = -2.93(3), and chi(cc) = -1.64(3) MHz, respectively. These values indicate that the nuclear contributions to the field electric gradient at the Xe nucleus are smaller than the electronic ones. (C) 2004 Elsevier B.V. All rights reserved.