Anion receptors that bind strongly to fluoride anions in organic solvents can help dissolve the lithium fluoride discharge products of primary carbon monofluoride (CFx) batteries, thereby preventing the clogging of cathode surfaces and improving ion conductivity. The receptors are also potentially beneficial to rechargeable lithium ion and lithium air batteries. We apply Density Functional Theory (DFT) to show that an oxalate-based pentafluorophenyl-boron anion receptor binds as strongly, or more strongly, to fluoride anions than many phenyl-boron anion receptors proposed in the literature. Experimental data shows marked improvement in electrolyte conductivity when this oxalate anion receptor is present. The receptor is sufficiently electrophilic that organic solvent molecules compete with F − for boron-site binding, and specific solvent effects must be considered when predicting its F − affinity. To further illustrate the last point, we also perform computational studies on a geometrically constrained boron ester that exhibits much stronger gas-phase affinity for both F − and organic solvent molecules. After accounting for specific solvent effects, however, its net F − affinity is about the same as the simple oxalate-based anion receptor. Finally, we propose that LiF dissolution in cyclic carbonate organic solvents, in the absence of anion receptors, is due mostly to the formation of ionic aggregates, not isolated F − ions.