  We investigate further a model of the accreting millisecond X-ray pulsars we
proposed earlier. In this model, the X-ray-emitting regions of these pulsars
are near their spin axes but move. This is to be expected if the magnetic poles
of these stars are close to their spin axes, so that accreting gas is channeled
there. As the accretion rate and the structure of the inner disk vary, gas is
channeled along different field lines to different locations on the stellar
surface, causing the X-ray-emitting areas to move. We show that this "nearly
aligned moving spot model" can explain many properties of the accreting
millisecond X-ray pulsars, including their generally low oscillation amplitudes
and nearly sinusoidal waveforms; the variability of their pulse amplitudes,
shapes, and phases; the correlations in this variability; and the similarity of
the accretion- and nuclear-powered pulse shapes and phases in some. It may also
explain why accretion-powered millisecond pulsars are difficult to detect, why
some are intermittent, and why all detected so far are transients. This model
can be tested by comparing with observations the waveform changes it predicts,
including the changes with accretion rate.
