  We generalize the problem of the coherent control of small quantum systems to
the case where the quantum bit (qubit) is subject to a fully general rotation.
Following the ideas developed in Pasini et al (2008 Phys. Rev. A 77, 032315),
the systematic expansion in the shortness of the pulse is extended to the case
where the pulse acts on the qubit as a general rotation around an axis of
rotation varying in time. The leading and the next-leading corrections are
computed. For certain pulses we prove that the general rotation does not
improve on the simpler rotation with fixed axis.
