  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 NaI 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.
