  We assess the cosmological variability of the fine-structure constant from
the analysis of an ensemble of Fe II absorption lines at the redshift z=1.15
toward the QSO HE 0515-4414 by means of the standard many-multiplet (MM)
technique and its revision based on linear regression (RMM). This is the first
time the MM technique is applied to exceptional high-resolution and high
signal-to-noise QSO spectra recorded with the UV-Visual Echelle Spectrograph
(UVES) at the ESO Very Large Telescope (VLT). Our analysis results in the most
stringent bounds hitherto infered from QSO absorption lines. Our results
support the null hypothesis of a non-varying fine-structure constant at a
significance level of 91 percent, whereas the support for the results presented
in former MM studies indicating a variation in the fine-structure constant is
12 percent.
