We show that a large class of multiperipheral models satisfy the bootstrap integral equation obtained by Krzywicki and Petersson and by Finkelstein and Peccei. We relate the leading-particle distribution directly to the parameters of the multiperipheral model. We present a simple one-dimensional model, closely related to the Chew-Pignotti model, for which the bootstrap equations are exactly soluble and we discuss the properties of the solution. We show how the bootstrap integral equations can be modified to provide a two-component model containing both pionization and diffraction.