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We present NLTE Li abundances for 88 stars in the metallicity range -3.5 < [Fe/H] < -1.0. The effective temperatures are based on the infrared flux method with improved values obtained mostly from interstellar D lines. The Li abundances were derived through MARCS models and high-quality UVES+VLT, HIRES+Keck and FIES+NOT spectra, and complemented with reliable equivalent widths from the literature. The less-depleted stars with [Fe/H] < -2.5 and [Fe/H] > -2.5 fall into two well-defined plateaus of ALi = 2.18 (σ = 0.04) and ALi = 2.27 (σ = 0.05), respectively. We show that the two plateaus are flat, unlike previous claims for a steep monotonic decrease in Li abundances with decreasing metallicities. At all metallicities we uncover a fine-structure in the Li abundances of Spite plateau stars, which we trace to Li depletion that depends on both metallicity and mass. Models including atomic diffusion and turbulent mixing seem to reproduce the observed Li depletion assuming a primordial Li abundance ALi = 2.64, which agrees well with current predictions (ALi = 2.72) from standard Big Bang nucleosynthesis. Adopting the Kurucz overshooting model atmospheres increases the Li abundance by +0.08 dex to ALi = 2.72, which perfectly agrees with BBN+WMAP.
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