Normal shock waves structured by nonequilibrium radiative and collisional ionization are solved analytically on the basis of a generalized radiation model. Just downstream of the interior embedded discontinuity, it is assumed and justified a posteriori that electron-atom collisional ionization to local thermodynamic equilibrium occurs over a length that is sufficiently small compared with the relevant one-step photon path. It is discovered that the appropriate emission-convection ratio is also a rather small quantity. Both small quantities lead to iterations studied to second approximation. The resulting shock morphology consists of a strong precursor, the embedded discontinuity, an inner collisional tail, and an outer radiative tail. Relevant calculations for helium are presented for a downstream degree of ionization of 0.8, an upstream temperature of 300 deg K, and upstream pressures of 10−3, 10−4, and 10−5 atm.