The most metal-poor damped Lyα system known to date, at z abs = 2.61843 in the spectrum of the QSO Q0913+072, with an oxygen abundance of only ∼1/250 of the solar value, shows six well-resolved D i Lyman series transitions in high-quality echelle spectra recently obtained with the European Southern Observatory (ESO) VLT. We deduce a value of the deuterium abundance log (D/H) = -4.56 ± 0.04 which is in good agreement with four out of the six most reliable previous determinations of this ratio in QSO absorbers. We find plausible reasons why in the other two cases the 1σ errors may have been underestimated by about a factor of two. The addition of this latest data point does not significantly change the mean value of the primordial abundance of deuterium, suggesting that we are now converging to a reliable measure of this quantity. We conclude that 〈log (D/H) p〉 = -4.55 ± 0.03 and Ωb,0h 2(BBN) = 0.0213 ± 0.0010 (68 per cent confidence limits). Including the latter as a prior in the analysis of the Wilkinson Microwave Anisotropy Probe (WMAP) five-year data leads to a revised best-fitting value of the power-law index of primordial fluctuations ns = 0.956 ± 0.013 (1σ) and ns < 0.990 with 99 per cent confidence. Considering together the constraints provided by WMAP 5, (D/H)p, baryon oscillations in the galaxy distribution, and distances to Type Ia supernovae, we arrive at the current best estimates Ωb,0h 2 = 0.0224 ± 0.0005 and ns = 0.959 ± 0.013.