The tracer exchange between a finite single-file channel (in which the diffusing guest particles are not able to pass each other) and its surroundings is considered. A mean-field calculation shows that the mean intracrystalline residence time tau(intra) is proportional to the 3rd power of the channel length L. Further, it is proportional to Theta/(1-Theta), where Theta denotes the relative occupancy. Monte Carlo simulations confirm these results to a satisfactory accuracy, especially at high occupancy. The essential mechanism of tracer exchange is considered in more detail.