Managing radiation risks typically involves establishing regulations that limit radiation exposure. The linear-no-threshold (LNT) dose-response model has been the traditional regulatory default assumption. According to the LNT model, for low a linear-energy-transfer (LET) radiation-induced stochastic effects (e.g., neoplastic transformation and cancer), the risk increases linearly without a threshold. Any radiation exposure is predicted to increase the number of cancer cases among a large population of people. Cancer risk extrapolation from high to low doses based on this model is widespread. Here, indirect evidence is provided that the excess cancer risk calculated at very low doses of low-LET radiation (e.g., around 1 mGy), based on extrapolating from high dose data for an irradiated human population using the LNT model, is likely a phantom excess risk. Indirect evidence is provided, suggesting that for brief exposures to low-LET radiation doses on the order of 1 mGy, that a decrease below the spontaneous level is many orders of magnitude more probable than for any increase in risk as would be predicted by extrapolating from high to low doses using the LNT model. Such a decrease is, however, not expected after exposure to high-LET alpha radiation. The risk reduction has been largely attributed to the induction of a protective apoptosis-mediated (PAM) process that selectively eliminates cells that contain genomic instability (e.g., mutant and neoplastically transformed cells). The PAM process appears to require a dose-rate-dependent stochastic threshold for activation whose minimum is estimated to possibly be as low as 0.01 mGy for X-rays and gamma rays. However, if the dose is too high (e.g., above 250 mGy for brief exposure at a high rate to X-rays or gamma rays), the PAM process is not expected to be activated. For protracted exposure to X-rays or gamma rays, doses as high as 400 mGy (and possibly higher) may activate the PAM process.