  We present an analysis of the nine type I X-ray bursts that were observed
from KS 1731-260 with RXTE. We find that the bursts divide naturally into two
populations: ``fast bursts'' occur on the Banana Branch when the accretion rate
is high and exhibit short decay times, high peak fluxes, and radius expansion
episodes. ``Slow bursts'' occur in the Island State at lower accretion rates,
have lower peak fluxes, higher fluences, longer decay times, and show no
evidence of radius expansion. All five of the fast bursts, and none of the four
slow bursts, show coherent oscillations near 524 Hz.
  We perform in-burst phase connection of the burst pulsations, which allows us
to unambiguously characterize their frequency evolution. That evolution
exhibits a variety of behaviors, including a sharp spin-down during one burst.
Applying our phase models, we find that the pulsations are spectrally harder
than the burst emission, with the strength of the pulsations increasing
monotonically with photon energy. Coherently summing all of the burst signals,
we find upper limits of ~5% relative to the strength of the main pulse on any
modulation at 1/2 or 3/2 the main pulse frequency. We discuss our results in
the context of models in which the burst pulsations are produced by a hot spot
on the surface of a spinning neutron star.
