  We present a refined phase-connected post-glitch ephemeris for the Geminga
pulsar that is a good fit to all the post-glitch data from EGRET, ASCA, and
XMM. We also present the results of phase-resolved spectroscopy of two XMM
X-ray observations of the Geminga pulsar obtained in 2002 and 2004. An
investigation is made into a previously claimed existence of a small hot spot
on the neutron star surface. We conclude that that interpretation was more
likely an artifact of an overly restrictive assumption used to fit the
phase-resolved spectra, namely, that the spectral index of the non-thermal
component is constant. When we allow the spectral index to vary as a function
of rotation phase, we find systematic variations in spectral index, and such
fits do not require an additional, hot blackbody component.
