We explore an odd class of quantum field theories where a hierarchy problem is resolved with new dynamics as opposed to new particles. The essential element of our construction is a U(1) pseudo-NambuGoldstone boson with symmetry breaking interactions all characterized by a large number N of units of the fundamental charge. In the resulting effective theory, quantum corrections, like those to the effective potential and mass, which are normally power divergent and saturated at the UV cutoff, are instead saturated at a much lower scale. This critical scale, which does not involve any new particle, corresponds to the onset of unsuppressed multiparticle production in scattering processes. Remarkably, this all happens within the tractable domain of weak coupling. Terms involving arbitrarily high powers of the Goldstone field must, however, be taken into account. In particular, a truncation to the renormalizable part of the effective Lagrangian would completely miss the physics.