Background: We are exposed to natural ionizing radiation and other genomic stressors throughout life and radiophobia has caused much harm to society. The main basis for radiophobia is the invalid linear no-threshold (LNT) hypothesis for cancer induction, which the System of Radiological Protection (SRP) is linked to. Largely unknown to the public, evolution-associated genomic stress adaptation (gensadaptation) over many previous generations now provides protection to all lifeforms from low radiation doses. Objective: To help bring about an improved SRP not linked to the invalid LNT hypothesis for radiation-caused health detriment and to promote low-dose radiation therapy for different diseases. Methods: All-solid-cancer mortality risk dose-response relationships for A-bomb survivors were generated based on published LNT-modeling-related results. Dose-response relationships for lung cancer prevention by low-dose radiation were generated by linear interpolation based on published data from a study using > 15,000 mice. Uncertainty characterization was based on Monte Carlo calculations for binomial and Poisson distributions. New dose characterization tools were used for threshold dose-response relationships for radiation-caused cancer mortality. Results: The all-solid-cancer mortality risk for A-bomb survivors transitioned from LNT to threshold-linear when adjusted for key missing uncertainty at low doses. The prevention of lung cancer in mice by low radiation doses depends on the radiation absorbed dose and type. Conclusions: The SRP should be linked to population dose thresholds rather than the invalid LNT hypothesis and small likely harmless radiation doses could possibly be used in treating different diseases.