Bloch and Nordsieck [Phys. Rev. 52, 54 (1937)] outlined a successive-approximation procedure for the calculation of finite infrared radiative corrections to the cross section for potential scattering of a Dirac electron, based on the use of coherent states for the description of the asymptotic motion of the electron in the presence of the radiation field and on the introduction of positive- and negative-energy projection operators. An elaboration of that procedure is described here in which the projection operators are used to develop an effective-Hamiltonian formulation of the scattering problem. This allows for a clear separation of the nearly singular contributions to the cross section from the remainder to which ordinary perturbation theory is applicable. With the aid of the optical theorem and the low-frequency approximation for single-photon spontaneous bremsstrahlung, a first-order correction to the Bloch-Nordsieck cross-section sum rule is obtained. The result is expressed in terms of measurable field-free scattering parameters. With the initial photon state chosen to be highly occupied, the formalism is directly applicable to the problem of scattering in an intense, slowly varying external field. Nearly singular terms arising from virtual Compton scattering in initial and final states, which appear when the field is not of the plane-wave type, are shown to cancel in the final form of the cross-section sum rule. This low-frequency approximation is then easily applied to problems involving realistically modeled fields in the form of wave packets, for example.