  We propose a new methodology for probing the cosmological variability of
alpha from pairs of FeII lines (SIDAM, single ion differential alpha
measurement) observed in individual exposures from a high resolution
spectrograph. By this we avoid the influence of the spectral shifts due to (i)
ionization inhomogeneities in the absorbers and (ii) non-zero offsets between
different exposures. Applied to the FeII lines of the metal absorption line
system at zabs = 1.839 in the spectrum of Q1101-264 obtained by means of the
UV-Visual Echelle Spectrograph (UVES) at the ESO Very Large Telescope (VLT),
SIDAM provides da/a = (2.4+/-3.8) 10^{-6}. The zabs = 1.15 FeII system toward
HE0515-4414 has been re-analyzed by this method thus obtaining for the combined
sample da/a = (0.4+/-1.5) 10^{-6}. These values are shifted with respect to the
Keck/HIRES mean da/a = (-5.7+/-1.1) 10^{-6} (Murphy et al. 2004) at very high
confidence level (95%). The fundamental photon noise limitation in the da/a
measurement with the VLT/UVES is discussed to figure the prospects for future
observations. It is suggested that with a spectrograph of 10 times the UVES
dispersion coupled to a 100m class telescope the present Oklo level (da/a >=
4.5 10^{-8}) can be achieved along cosmological distances with differential
measurements of da/a.
