Increasing protein stability is interesting for practical reasons and because it tests our understanding of protein energetics. We explore here the feasibility of stabilizing proteins by replacing underexposed polar residues by apolar ones of similar size and shape. We have compared the stability of wild-type apoflavodoxin with that of a few carefully selected mutants carrying Y → F, Q → L, T → V or K → M replacements. Although a clear inverse correlation between native solvent exposures of replaced polar residues and stability of mutants is observed, most mutations fail to stabilize the protein. The promising exceptions are the two Q → L mutations tested, which characteristically combine the greatest reduction in polar burial with the greatest increase in apolar burial relative to wild type. Analysis of published stability data corresponding to a variety of mutant proteins confirms that, unlike Y → F or T → V replacements, Q → L mutations tend to be stabilizing, and it suggests that N → L mutations might be stabilizing as well. On the other hand, we show that the stability changes associated to the apoflavodoxin mutations can be rationalized in terms of differential polar and apolar burials upon folding plus a generic destabilizing penalty term. Simple equations combining these contributions predict stability changes in a large data set of 113 mutants (Y → F, Q → L or T → V) similarly well as more complex algorithms available on the Internet.