The COMPLIS (COllaboration for spectroscopic Measurements using a Pulsed-Laser Ion Source) experiment is carried out at the ISOLDE-Booster facility at CERN. The aim is to measure the hyperfine structure and the isotope shift of a series of radioactive laser-desorbed atoms by multiple-step laser ionization. This technique is especially suitable for refractory elements not directly available as beams from the isotope separator. By collecting a primary radioactive beam, it is possible to delay the laser desorption as long as necessary to obtain the particular daughter of interest. Laser spectroscopy measurements have been carried out on very neutron-deficient gold, platinum and iridium isotopes. Magnetic moments mu(I), spectroscopic quadrupole moments Q(s) and changes of the nuclear mean square charge radius delta[r(c)(2)] along each isotopes series have been extracted. From some results, a detailed comparison with the predictions of the models is presented.