  We present an analysis of 23 absorption systems along the lines of sight
towards 18 quasars in the redshift range of $0.4 \leq z_{abs} \leq 2.3$
observed on the Very Large Telescope (VLT) using the Ultraviolet and Visual
Echelle Spectrograph (UVES). Considering both statistical and systematic error
contributions we find a robust estimate of the weighted mean deviation of the
fine-structure constant from its current, laboratory value of
$\Delta\alpha/\alpha=\left(0.22\pm0.23\right)\times10^{-5}$, consistent with
the dipole variation reported in Webb et al. and King et al. This paper also
examines modelling methodologies and systematic effects. In particular we focus
on the consequences of fitting quasar absorption systems with too few absorbing
components and of selectively fitting only the stronger components in an
absorption complex. We show that using insufficient continuum regions around an
absorption complex causes a significant increase in the scatter of a sample of
$\Delta\alpha/\alpha$ measurements, thus unnecessarily reducing the overall
precision. We further show that fitting absorption systems with too few
velocity components also results in a significant increase in the scatter of
$\Delta\alpha/\alpha$ measurements, and in addition causes
$\Delta\alpha/\alpha$ error estimates to be systematically underestimated.
These results thus identify some of the potential pitfalls in analysis
techniques and provide a guide for future analyses.
