The β-correction to the Hartmann-Tran (HT) profile, recently introduced to model the spectral shape of a molecular transition strongly affected by the Dicke narrowing effect (Konefal et al., JQSRT 242 (2020) 106784), the HT profile (Ngo et al., JQSRT 129 (2013) 89), and the speed dependent (complex) hard collision model (SDcHC, in which the velocity changing collision rate is characterized by a complex number) are tested using spectra of two rovibrational lines of HCl. The R(5) and R(9) lines of the fundamental band of HCl broadened by He, Ar and SF 6 have been recorded with a difference-frequency laser spectrometer for total pressures ranging from 12 to 930 mbar. These lines, measured in large pressure ranges with different collision-partners provide a meaningful test of the above-mentioned line-shape models. The results confirm that non-Voigt effects are significant for HCl broadened by Ar and SF 6 and mainly due to the large influence of the Dicke narrowing effect. For HCl-SF 6 and HCl-Ar, especially for the R(9) line, using the β-correction together with the HT profile (and with the speed-dependent hard collision model, SDHC) significantly improves the fit residuals while it has no effect on (or tends to deteriorate) the quality of the fit for HCl-He and for the R(5) line of HCl-SF 6 , for which the influence of velocity changing collisions is smaller. Except for HCl-He, the SDcHC model leads to better quality of fit compared to the HT profile. The results also show that numerical correlations between refined line-shape parameters of the HT profile are important and can lead to ill-determined parameters while they are more properly determined with the SDcHC model.