  We have previously presented 5.7-sigma evidence for a smaller alpha at
redshifts 0.2 < z_abs < 3.7 from a sample of 128 Keck/HIRES quasar absorption
systems: da/a = (-0.57 +/- 0.10) x 10^{-5}. A non-zero da/a manifests itself as
a distinct pattern of shifts in the measured absorption line wavelengths. The
statistical error is now small: we do detect small line shifts in the HIRES
data. Whether these shifts are due to systematic errors or due to real
variation in alpha is now the central question. Here we summarize the two
potentially most important systematic effects: atmospheric dispersion and
isotopic abundance evolution. Previously, these have been difficult to
quantify/model but here we find that neither of them can explain our results.
Furthermore, the HIRES spectra themselves contain no evidence for these
effects. Independent measurements of da/a with a different telescope and
spectrograph are now crucial if we are to rule out or confirm the present
evidence for a variable alpha.
