  Comparison of quasar absorption line spectra with laboratory spectra provides
a precise probe for variability of the fine structure constant, alpha, over
cosmological time-scales. We constrain variation in alpha in 21 Keck/HIRES Si
IV absorption systems using the alkali doublet (AD) method in which changes in
alpha are related to changes in the doublet spacing. The precision obtained
with the AD method has been increased by a factor of 3: da/a = (-0.5 +/- 1.3) *
10^{-5}. We also analyse potential systematic errors in this result. Finally,
we compare the AD method with the many-multiplet method which has achieved an
order of magnitude greater precision and we discuss the future of the AD
method.
