Quasimonochromatic x rays are difficult to produce above 100 keV, but have a number of uses in x-ray and nuclear science, particularly in the analysis of transuranic species. Inverse Compton scattering (ICS) is capable of fulfilling this need, producing photon beams with properties and energies well beyond the limits of typical synchrotron radiation facilities. We present the design and predicted output of such an ICS source at CBETA, a multiturn energy-recovery linac with a top energy of 150 MeV, which we anticipate producing x rays with energies above 400 keV and a collimated flux greater than 108 photons per second within a 0.5% bandwidth. At this energy, the anticipated flux exceeds that attainable from storage ring sources of synchrotron radiation, even though CBETA is a significantly smaller accelerator system. We also consider the consequences of extending the CBETA ICS source performance to higher electron energies, exploring achievable parameters and applications for MeV-scale photons. We foresee that future energy-recovery linacs may serve as ICS sources, capable of providing high energy photons unavailable at synchrotron radiation facilities or photon beams above approximately 300 keV which outperform sources at synchrotron radiation facilities in both flux and average brilliance. © 2021 authors.