Following earlier studies, it is argued that internal waves propagating in weakly stratified layers are affected by the Coriolis terms proportional to the cosine of latitude (which are neglected in the so-called Traditional Approximation). A systematic overview is given of the wave properties if these terms are included. The usage of characteristics and vertical modes is compared and contrasted. It is shown that the ratio of potential and kinetic energy varies horizontally if more than one mode is considered. For many modes, the energy becomes organized in beams, within which the ratio approaches the values obtained from the characteristics. The polarization of the horizontal velocity field also undergoes qualitative changes due to 'non-traditional' effects. In particular, the horizontal direction of wave propagation can no longer be inferred from the orientation of the major axis of the ellipse; also, the polarization may now become counterclockwise in the Northern Hemisphere. Finally, the propagation through layers of different stratification is examined by means of a transmission coefficient. It is shown that the near-inertial band is special because it is transmitted through layers of any stratification. The implications for internal-wave observations are discussed.