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 \simeq 6 \times 10 ^ { 4 } 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 can not 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 .