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The presence of 6Li in the atmospheres of metal-poor halo stars is usuallyinferred from the detection of a subtle extra depression in the red wing of the7Li doublet line at 670.8 nm. However, the intrinsic line asymmetry caused byconvective flows in the photospheres of cool stars is almost indistinguishablefrom the asymmetry produced by a weak 6Li blend on a (presumed) symmetric 7Liprofile. Previous determinations of the 6Li/ 7Li isotopic ratio based on 1Dmodel atmospheres, ignoring the convection-induced line asymmetry, musttherefore be considered as upper limits. By comparing synthetic 1D LTE and 3Dnon-LTE line profiles of the Li 670.8 nm feature, we quantify the differentialeffect of the convective line asymmetry on the derived 6Li abundance as afunction of effective temperature, gravity, and metallicity. As expected, wefind that the asymmetry effect systematically reduces the resulting 6Li/7Liratios. Depending on the stellar parameters, the 3D-1D offset in 6Li/7Li rangesbetween -0.005 and -0.020. When this purely theoretical correction is takeninto account for the Asplund 2006 sample of stars, the number of significant6Li detections decreases from 9 to 5 (2 sigma criterion), or from 5 to 2 (3sigma criterion).  We also present preliminary results of a re-analysis of high-resolution, highS/N spectra of individual metal-poor turn-off stars, to see whether the "secondLithium problem" actually disappears when accounting properly for convectionand non-LTE line formation in 3D stellar atmospheres. Out of 8 stars, HD84937seems to be the only significant (2 sigma) detection of 6Li. In view of ourresults, the existence of a 6Li plateau appears questionable.

6Li detection in metal-poor stars: can 3D model atmospheres solve the second lithium problem?