When a shock wave moving through an isentropic ideal gas catches up with, and passes into a simple expansion wave, the shock decays. Because of this the gas will not be isentropic in the region behind the shock. The problem of determining the motion of the gas in this region is as yet unsolved. In this paper we introduce a simple compression wave behind the shock which catches up with it at the instant of its entry into the leading expansion wave. This second wave is chosen so as to counteract the decaying effect of the first, and keep the shock strength constant throughout the motion. We assume the first wave to be point-centred, and caused by the withdrawal of a piston at a finite velocity from a gas at rest in a shock tube. After a finite time the piston is halted causing the shock. The problem is then to determine the subsequent motion of the piston to produce a compression wave with the desired property.