Standard volumes for atoms in double-stranded B-DNA are derived using high resolution crystal structures from the Nucleic Acid Database (NDB) and compared with corresponding values derived from crystal structures of small organic compounds in the Cambridge Structural Database (CSD). Two different methods are used to compute these volumes: the classical Voronoi method, which does not depend on the size of atoms, and the related Radical Planes method which does. Results show that atomic groups buried in the interior of double-stranded DNA are, on average, more tightly packed than in related small molecules in the CSD. The packing efficiency of DNA atoms at the interfaces of 25 high resolution protein-DNA complexes is determined by computing the ratios between the volumes of interfacial DNA atoms and the corresponding standard volumes. These ratios are found to be close to unity, indicating that the DNA atoms at protein-DNA interfaces are as closely packed as in crystals of B-DNA. Analogous volume ratios, computed for buried protein atoms, are also near unity, confirming our earlier conclusions that the packing efficiency of these atoms is similar to that in the protein interior. In addition, we examine the number, volume and solvent occupation of cavities located at the protein-DNA interfaces and compared them with those in the protein interior. Cavities are found to be ubiquitous in the interfaces as well as inside the protein moieties. The frequency of solvent occupation of cavities is however higher in the interfaces, indicating that those are more hydrated than protein interiors. Lastly, we compare our results with those obtained using two different measures of shape complementarity of the analysed interfaces, and find that the correlation between our volume ratios and these measures, as well as between the measures themselves, is weak. Our results indicate that a tightly packed environment made up of DNA, protein and solvent atoms plays a significant role in protein-DNA recognition.