  We introduce a model which allows the fine structure constant (alpha) to vary
throughout space and time due to a coupling to a scalar field with a
non-canonical kinetic structure. This provided a new extension of the
Bekenstein-Sandvik-Barrow-Magueijo model of alpha variations. The background
cosmology is studied in detail using dynamical systems techniques for a scalar
field of ghost condensate type. We show generically that if the kinetic terms
are chosen to allow an accelerated late-time attractor for the expansion scale
factor then alpha will not asymptote to a constant at late times.
