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Current analyses of VLT/UVES quasar spectra disagree with the Keck/HIRESevidence for a varying fine-structure constant, alpha. To investigate this weintroduce a simple method for calculating the minimum possible uncertainty onDelta(alpha)/alpha for a given quasar absorber. For many absorbers in Chand etal. (2004) and for the single-absorber constraint of Levshakov et al. (2006)the quoted uncertainties are smaller than the minimum allowed by the UVES data.Failure of this basic consistency test prevents reliable comparison of the UVESand HIRES results.Comment: 4 pages, 2 figures (3 EPS files). Invited contribution to the  proceedings of "Precision Spectroscopy in Astrophysics", Aveiro, Portugal,  Sep. 2006, eds Pasquini et al., ESO Astrophysics Symposia. v2: Corrected  small typos and a reference. v3: Corrected another small typ

Revisiting VLT/UVES Constraints on a Varying Fine-structure Constant