Standard stellar evolution predicts that F stars should retain their initial surface lithium (Li) abundance because their convection zones are too shallow to destroy it at their base. Yet, observations reveal a severe Li depletion (the “Boesgaard Gap”), perhaps by as much as about two orders of magnitude, in a narrow Teff range. Several physical mechanisms, not usually included in stellar evolution calculations, have been proposed to account for this Li deficiency. These include diffusion, mass loss, meridional circulation, and rotationally-induced mixing driven by angular momentum loss. Identifying which of these (if any) might really be at work is not only of vital interest to stellar evolution, but may also have serious implications elsewhere (e.g. cosmology, Deliyannis et al. 1991). We bring attention to beryllium (Be) observations in F stars, which are crucial for discriminating between scenarios. Particularly important is the star 110 Her, which is depleted in Be by about a factor of 5 -10, but still has a detectable Li abundance (depleted by a factor of 100 - 200). Depleting surface Be without having depleted nearly all of the surface Li requires specific circumstances; we discuss how this depletion property severely constrains or eliminates most of the proposed mechanisms. One mechanism, rotationally-induced mixing, predicts relative depletions for these elements that agree well with what is observed.