  We analyze the properties of the pulsed emission from the accreting
millisecond pulsar SAX J1808.4-3658 in observations of its April 1998 outburst
by the Rossi X-Ray Timing Explorer. Pulse phase spectroscopy shows that the
emission evolves from a hard spectrum (power law with photon index 2.39+-0.06)
to a soft spectrum (index 3.39+-0.24). This softening is also observable as a
phase lag in the fundamental of low-energy photons with respect to high-energy
photons. We show that this lag is roughly constant over ten days of the
outburst. We fit these data with a model where the pulse emission is from a hot
spot on the rotating neutron star and the flux as a function of phase is
calculated including the effects of general relativity. The energy-dependent
lags are very well described by this model. The harder spectra at earlier
phases (as the spot approaches) are the result of larger Doppler boosting
factors which are important for this fast pulsar.
