We discuss the implications of maintaining finite mass renormalization when the wave-function renormalization constant Z3 of an elementary particle is set equal to zero, making only the approximations of two-particle unitarity. We show that this defines a field-theory bootstrap for the elementary particle which is completely equivalent to the usual type of bootstrap based on the ND method. As Z3 goes to zero the vertex function and inverse propagator develop poles which move to μ2, the elementary-particle mass, in the limit. For nonzero Z3 this pole does not contribute to the scattering amplitude, but at Z3=0 it cancels the elementary-particle pole in the single-particle reducible part, leaving the dynamical pole in the irreducible part. We suggest, further, that in this limit the bootstrapped state is a Regge pole.