  We consider smooth time-changes of the classical horocycle flows on the unit
tangent bundle of a compact hyperbolic surface and prove sharp bounds on the
rate of equidistribution and the rate of mixing. We then derive results on the
spectrum of smooth time-changes and show that the spectrum is absolutely
continuous with respect to the Lebesgue measure on the real line and that the
maximal spectral type is equivalent to Lebesgue.
