Eigenvolume effects in the hadron resonance gas (HRG) model are studied for experimental hadronic yields in nucleus–nucleus collisions. If particle eigenvolumes are different for different hadron species, the excluded volume HRG (EV-HRG) improves fits to multiplicity data. In particular, using different mass–volume relations for strange and non-strange hadrons we observe a remarkable improvement in the quality of the fits. This effect appears to be rather insensitive to other details in the schemes employed in the EV-HRG. We show that the parameters found from fitting the data of the ALICE Collaboration in central Pb+Pb collisions at the collision energy $\sqrt{s_{\rm NN}} = 2.76$~TeV entail the same improvement for all centralities at the same collision energy, and for the RHIC and SPS data at lower collision energies. Our findings are put in the context of recent fits of lattice QCD results.