The cosmological variability of $\alpha$ is probed from individual observations of pairs of Fe II lines. This procedure allows a better control of the systematics and avoids the influence of the spectral shifts due to ionisation inhomogeneities in the absorbers and/or non-zero offsets between different exposures. Applied to the Fe II lines of the metal absorption systems at $z_{\rm abs}=1.839$ in Q1101–264 and at $z_{\rm abs}=1.15$ in HE0515–4414 observed by means of UVES at the ESO-VLT, it provides $\Delta\alpha/\alpha = (0.4\pm1.5_{\rm stat})\times10^{-6}$. The result is shifted with respect to the Keck/HIRES mean $\Delta\alpha/\alpha = (-5.7\pm1.1_{\rm stat})\times10^{-6}$ (Murphy et al. 2004) at a high confidence level (95%). Full details of this work are given in Levshakov et al. (2005).