  We consider smooth complete solutions to Ricci flow with bounded curvature on
manifolds without boundary in dimension three. Assuming an open ball at time
zero of radius one has curvature bounded from below by -1, then we prove
estimates which show that compactly contained subregions of this ball will be
smoothed out by the Ricci flow for a short but well defined time interval. The
estimates we obtain depend only on the initial volume of the ball and the
distance from the compact region to the boundary of the initial ball. Versions
of these estimates for balls of radius r follow using scaling arguments.
