We have performed experiments using a three-dimensional Bose-Einstein condensate of sodium atoms in a one-dimensional optical lattice to explore some unusual properties of band structure. In particular, we investigate the loading of a condensate into a moving lattice and find nonintuitive behavior. We also revisit the behavior of atoms, prepared in a single quasimomentum state, in an accelerating lattice. We generalize this study to a cloud whose atoms have a large quasimomentum spread, and show that the cloud behaves differently from atoms in a single Bloch state. Finally, we compare our findings with recent experiments performed with fermions in an optical lattice.