Recent work by Webb et al. has provided indications of spatial variations of the fine-structure constant, α, at a level of a few parts per million. Using a dataset of 293 archival measurements, they further show that a dipole provides a statistically good fit to the data, a result subsequently confirmed by other authors. Here we show that a more recent dataset of dedicated measurements further constrains these variations: although there are only 10 such measurements, their uncertainties are considerably smaller. We find that a dipolar variation is still a good fit to the combined dataset, but the amplitude of such a dipole must be somewhat smaller: 8.1 ± 1.7 ppm for the full dataset, versus 9.4 ± 2.2 ppm for the Webb et al. data alone, both at the 68.3% confidence level. Constraints on the direction on the sky of such a dipole are also significantly improved. On the other hand the data can't yet discriminate between a pure spatial dipole and one with an additional redshift dependence.