Deuterium abundance re-measurements by Burles and Tytler (1998; hereafter BT) yielded D/H = (3.3 +/- 0.3) 10^{-5} and the robust upper limit D/H < 3.9 10^{-5} from the z_a = 3.572 system toward Q1937-1009. In this new analysis BT adopted multicomponent microturbulent models together with the possibility to vary freely the local continuum level around each HI line to improve the fit. The procedure failed, however, to fit adequately D Ly-beta without recourse to an additional H Ly-alpha contamination at the position of D Ly-beta. We show that this obstacle may be successfully overcome within the framework of the mesoturbulent model accounting (in contrast to the microturbulent approximation) for a correlated structure of the large scale velocity field. Using the same observational data and the original continuum as determined by Tytler et al. (1996), we obtained good fits. The one-component mesoturbulent models provide D/H in the range (3.2 - 4.8) 10^{-5} and the total hydrogen column density N(HI) = (5.6 - 7.0) 10^{17} cm^{-2}. This result is consistent with that found by us from the z_a = 2.504 and z_a = 0.701 systems toward Q1009+2956 and Q1718+4807, respectively. The range for D/H common to all three analyses is D/H = (4.1 - 4.6) 10^{-5}. This value is consistent with standard big bang nucleosynthesis [SBBN] if the baryon-to-photon ratio, eta, is in the range 4.2 10^{-10} <= eta <= 4.6 10^{-10}, implying 0.0155 <= Omega_b h^2_{100} <= 0.0167.
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