  Large statistical samples of quasar spectra have previously indicated
possible cosmological variations in the fine-structure constant, $\alpha$. A
smaller sample of higher signal-to-noise ratio spectra, with dedicated
calibration, would allow a detailed test of this evidence. Towards that end, we
observed equatorial quasar HS 1549$+$1919 with three telescopes: the Very Large
Telescope, Keck and, for the first time in such analyses, Subaru. By directly
comparing these spectra to each other, and by `supercalibrating' them using
asteroid and iodine-cell tests, we detected and removed long-range distortions
of the quasar spectra's wavelength scales which would have caused significant
systematic errors in our $\alpha$ measurements. For each telescope we measure
the relative deviation in $\alpha$ from the current laboratory value,
$\Delta\alpha/\alpha$, in 3 absorption systems at redshifts
$z_{\mathrm{abs}}=1.143$, 1.342, and 1.802. The nine measurements of
$\Delta\alpha/\alpha$ are all consistent with zero at the 2-$\sigma$ level,
with 1-$\sigma$ statistical (systematic) uncertainties 5.6--24 (1.8--7.0) parts
per million (ppm). They are also consistent with each other at the 1-$\sigma$
level, allowing us to form a combined value for each telescope and, finally, a
single value for this line of sight: $\Delta\alpha/\alpha=-5.4 \pm
3.3_{\mathrm{stat}} \pm 1.5_{\mathrm{sys}}$ ppm, consistent with both zero and
previous, large samples. We also average all Large Programme results measuring
$\Delta\alpha/\alpha=-0.6 \pm 1.9_{\mathrm{stat}} \pm 0.9_{\mathrm{sys}}$ ppm.
Our results demonstrate the robustness and reliability at the 3 ppm level
afforded by supercalibration techniques and direct comparison of spectra from
different telescopes.
