  We study the energy spectrum and wave packet dynamics of electrons in a
two-dimensional periodic potential subject to a perpendicular spatially
modulated magnetic field. We observe avoided band crossings, metal-insulator
transitions, and changes in the spreading direction of wave packets in two new
situations: (i) for a purely magnetic modulation and (ii) in the limit of weak
electric and magnetic modulations, where the Landau band coupling can be
neglected. In the second case the corresponding classical system is no longer
chaotic but integrable, whereby these phenomena are not expected. We argue that
they are due to tunneling.
