  Angular momentum loss in ultracompact binaries, such as the AM Canum
Venaticorum stars, is usually assumed to be due entirely to gravitational
radiation. Motivated by the outflows observed in ultracompact binaries, we
investigate whether magnetically coupled winds could in fact lead to
substantial additional angular momentum losses. We remark that the scaling
relations often invoked for the relative importance of gravitational and
magnetic braking do not apply, and instead use simple non-empirical expressions
for the braking rates. In order to remove significant angular momentum, the
wind must be tied to field lines anchored in one of the binary's component
stars; uncertainties remain as to the driving mechanism for such a wind. In the
case of white dwarf accretors, we find that magnetic braking can potentially
remove angular momentum on comparable or even shorter timescales than
gravitational waves over a large range in orbital period. We present such a
solution for the 17-minute binary AM CVn itself which admits a cold white dwarf
donor and requires that the accretor have surface field strength ~6E4 G. Such a
field would not substantially disturb the accretion disk. Although the
treatment in this paper is necessarily simplified, and many conditions must be
met in order for a wind to operate as proposed, it is clear that magnetic
braking cannot easily be ruled out as an important angular momentum sink. We
finish by highlighting observational tests that in the next few years will
allow an assessment of the importance of magnetic braking.
