Light-front field theory may provide a promising avenue of research for nuclear and particle physics, but a Tamm-Dancoff truncation of field theory is required for practical computations. Such a truncation limits the number of virtual mesons allowed in hadronic field theories, or the number of quarks and gluons allowed in bound states described by quantum chromodynamics. Past Tamm-Dancoff renormalization problems are analyzed and a solution is proposed.