This paper presents uniform error bounds for fast calculation of approximate Voigt profiles that can be useful with the computationally demanding broadband line-by-line analysis of radiative transfer in the atmosphere. Formal proofs are given and rigorous criteria are provided to determine the domain on which the Voigt profile can be approximated by the Lorentz profile within any required accuracy. The most accurate Voigt-implementation to date can then be used to determine the required threshold parameters. Since most of the broadband radiative transfer calculations in the atmosphere will pertain to far wing computations, the potential saving in time is almost the same as by replacing the Voigt computation for the Lorentzian altogether completely. The error bounds can furthermore be used to derive a simple and efficient subband adaptive line selection strategy which can be used to rigorously exclude lines that will contribute to the resulting absorption coefficient less than any given threshold.