The first iterate solution of the Boltzmann equation is given for an impulsively started, specularly reflecting piston. An approximation for each collision operator that preserves the significant contribution from each of the fourteen collision classes which are generated by the single discontinuity in momentum space is obtained. Five of the sevenfold integrals appearing in the expressions for the first iterate moments are evaluated in closed form and the remaining two integrals are evaluated numerically. This iterative solution is valid for large departures from equilibrium, and, to the order to which the iteration has been carried, to times of the order of one or two mean free times between collisions.