  The presence of 6Li in the atmospheres of metal-poor halo stars is usually
inferred from the detection of a subtle extra depression in the red wing of the
7Li doublet line at 670.8 nm. However, the intrinsic line asymmetry caused by
convective flows in the photospheres of cool stars is almost indistinguishable
from the asymmetry produced by a weak 6Li blend on a (presumed) symmetric 7Li
profile. Previous determinations of the 6Li/ 7Li isotopic ratio based on 1D
model atmospheres, ignoring the convection-induced line asymmetry, must
therefore be considered as upper limits. By comparing synthetic 1D LTE and 3D
non-LTE line profiles of the Li 670.8 nm feature, we quantify the differential
effect of the convective line asymmetry on the derived 6Li abundance as a
function of effective temperature, gravity, and metallicity. As expected, we
find that the asymmetry effect systematically reduces the resulting 6Li/7Li
ratios. Depending on the stellar parameters, the 3D-1D offset in 6Li/7Li ranges
between -0.005 and -0.020. When this purely theoretical correction is taken
into account for the Asplund 2006 sample of stars, the number of significant
6Li detections decreases from 9 to 5 (2 sigma criterion), or from 5 to 2 (3
sigma criterion).
  We also present preliminary results of a re-analysis of high-resolution, high
S/N spectra of individual metal-poor turn-off stars, to see whether the "second
Lithium problem" actually disappears when accounting properly for convection
and non-LTE line formation in 3D stellar atmospheres. Out of 8 stars, HD84937
seems to be the only significant (2 sigma) detection of 6Li. In view of our
results, the existence of a 6Li plateau appears questionable.
