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 E ( B - V ) values obtained mostly from interstellar Na i 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 A _ { Li } = 2.18 ( \sigma = 0.04 ) and A _ { Li } = 2.27 ( \sigma = 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 A _ { Li } = 2.64 , which agrees well with current predictions ( A _ { Li } = 2.72 ) from standard Big Bang nucleosynthesis . Adopting the Kurucz overshooting model atmospheres increases the Li abundance by +0.08 dex to A _ { Li } = 2.72 , which perfectly agrees with BBN+WMAP .