The spectroscopic quadrupole moments of the neutron deficient radioactive Ir isotopes Os), for which K 0 and 1 is expected. In the framework of the rotational model the K-quantum number can be determined from the spectroscopic quadrupole moment Q which is connected with the intrinsic quadrupole moment Q 0 byThus, for a low-K state of a nucleus with prolate deformation, a negative quadrupole moment is expected. For 186 Ir, this was confirmed by the measurement of the spectroscopic quadrupole moment with quadrupole-interaction nuclear orientation (QI-NO), which yielded Q 22. 41͑20͒ b [3]. This value indicated a larger nuclear deformation than expected from the extrapolation of heavier Ir isotopes. In this context, it is an interesting question whether the nuclear deformation of the low-K anomalous ground state 186 Ir g is enhanced by the specific properties of the p1͞2 2 ͓541͔ proton intruder state coming down from the ph 9͞2 orbital. This can be tested by a measurement of the quadrupole moment of the low- Os), for which K 4 and 5 is expected. Recently, from spectroscopic investigations, the configuration and even the assignment of I 5 for 184 Ir was doubted [7]. Here, in addition to precision measurements of quadrupole moments, we present a new method for the measurement of ground state spins with resonance precision. It is based on the following features: For the case of a combined magnetic-dipole plus electric-quadrupole hyperfine interaction the resonance spectrum consists of 2I subresonances which are separated equidistantly around the magnetic hyperfine splitting. The frequency offset of the subresonance with the largest amplitude to the magnetic hyperfine splitting depends on I. Thus I can be determined by frequency measurements. This method was applied to 184 Ir, with the unambiguous result I 5. The questions addressed above can be answered by measuring the quadrupole splittings in hcp-Co, from which-without the exact knowledge of the electric field gradient (EFG) of Ir in hcp-Co-highly precise ratios of quadrupole moments are obtained. We also present, however, results of quadrupole-interaction-resolved NMR on oriented nuclei (QI-NMR-ON) measurements on 187 Ir known from muonic x-ray spectroscopy [9], we are able to determine 5016 0031-9007͞96͞77(25)͞5016(4)$10.00