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 binarys 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.
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