A more complete radiation treatment is introduced into the zero-dimensional magnetized fuel inertial confinement fusion (ICF) model of Lindemuth and Kirkpatrick. In particular, the effects of synchrotron radiation and the inverse Compton effect are considered. Only slight changes in the high gain regions of initial shell velocity/initial fuel density parameter space were observed. This more complete radiation treatment removes some objections to the Lindemuth-Kirkpatrick model and lends further support to the idea that magnetic thermal insulation can significantly reduce driver requirements for ICF targets.