  We discuss how laboratory experiments can be used to place constraints on
possible variations of the fine structure constant alpha in the observationally
relevant redshift interval z ~= 0 - 5, within a rather general theoretical
framework. We find a worst case upper limit for Delta alpha / alpha of 8 x
10^-6 for z <= 5 and Delta alpha / alpha of 0.9 x 10^-6 for z <= 1.6. The
derived limits are at variance with the recent findings by Webb et al. (1998),
who claim an observed variation of Delta alpha/alpha = -2.6 +- 0.4 x 10^-5 at
1<z<1.6.
