There has recently been interest in the role of inverse bremsstrahlung, the emission of photons by fast suprathermal ions in collisions with ambient electrons possessing relatively low velocities, in tenuous plasmas in various astrophysical contexts. This follows a long hiatus in the application of suprathermal ion bremsstrahlung to astrophysical models since the early 1970s. The potential importance of inverse bremsstrahlung relative to normal bremsstrahlung, i.e., where ions are at rest, hinges upon the underlying velocity distributions of the interacting species. In this paper, we identify the conditions under which the inverse bremsstrahlung emissivity is significant relative to that for normal bremsstrahlung in shocked astrophysical plasmas. We determine that, since both observational and theoretical evidence favors electron temperatures almost comparable to, and certainly not very deficient relative to, proton temperatures in shocked plasmas, these environments generally render inverse bremsstrahlung at best a minor contributor to the overall emission. Hence, inverse bremsstrahlung can be safely neglected in most models invoking shock acceleration in discrete sources such as supernova remnants. However, on scales >~100 pc distant from these sources, Coulomb collisional losses can deplete the cosmic-ray electrons, rendering inverse bremsstrahlung, and perhaps bremsstrahlung from knock-on electrons, possibly detectable.