  We propose a collective Hamiltonian which incorporates the standard
quadrupole terms, octupole terms classified according to the irreducible
representations of the octahedron group, a quadrupole-octupole interaction, as
well as a term for the bandhead energy linear in K (the projection of angular
momentum on the body-fixed z-axis). The energy is subsequently minimized with
respect to K for each given value of the angular momentum I, resulting in K
values increasing with I within each band, even in the case in which K is
restricted to a set of microscopically plausible values. We demonstrate that
this Hamiltonian is able to reproduce a variety of ``beat'' patterns observed
recently for the odd-even staggering in octupole bands of light actinides.
