We have recently shown that protein folding is driven by the water-entropy gain. When the alpha-helix or beta-sheet is formed, the excluded volumes generated by the backbone and side chains overlap, leading to an increase in the total volume available to the translational displacement of water molecules. Primarily by this effect, the water entropy becomes higher. At the same time, the dehydration penalty (i.e., the break of hydrogen bonds with water molecules) is compensated by the formation of intramolecular hydrogen bonds. Hence, these secondary structures are very advantageous units, which are to be formed as much as possible in protein folding. The packing of side chains, which leads to a large increase in the water entropy, is also crucially important. Here we investigate the roles of the side-chain packing in the second structural preference in protein folding. For some proteins we calculate the hydration entropies of a number of structures including the native structure with or without side chains. A hybrid of the angle-dependent integral equation theory combined with the multipolar water model and the morphometric approach is employed in the calculation. Our major findings are as follows. For the structures without side chains, there is an apparent tendency that the water entropy becomes higher as the alpha-helix or beta-sheet content increases. For the structures with side chains, however, a higher content of alpha-helices or beta-sheets does not necessarily lead to larger entropy of water due to the effect of the side-chain packing. The thorough, overall packing of side chains, which gives little space in the interior, is unique to the native structure. To accomplish such specific packing, the alpha-helix and beta-sheet contents are prudently adjusted in protein folding.