Significant effects on the developing human brain of exposure to ionizing radiation are seen among individuals exposed in the 8th-25th week after ovulation. These effects, particularly in the highly vulnerable period of 8-15 weeks after ovulation, manifest themselves most dramatically as an increased frequency of severe mental retardation. However, the distribution of cases of severe mental retardation suggests a threshold in the low-dose region. The 95% lower bound of the threshold in those survivors exposed 8-15 weeks after ovulation was zero for the individual data based on the simple linear model, and 0.15 Gy based on the exponential linear model used in our previous report (1987), but the 95% lower bound of the threshold based on all of the data including 21 additional cases with known doses appears to be 0.05 Gy using the maximum likelihood estimates derived from an exponential-linear model. The latter model was selected because it provides the best fit from the standpoint of the stableness and reasonableness of the estimates among the five models applied to the data. When two probably non-radiation-related cases of Down's syndrome are excluded from the 19 mentally retarded cases exposed 8-15 weeks post ovulation, the 95% lower bound of the threshold is in the range of 0.15-0.25 Gy based on the exponential-linear model used in 1987, but is in the range of 0.06-0.31 Gy when the more reasonable and better model applied here is used. For exposure in the 16-25-week period based on the same model, the 95% lower bound of the threshold changed from 0.25 to 0.28 Gy, both with and without inclusion of the two probable non-radiation-related mentally retarded cases; one of these cases was probably familial in origin since there was a retarded sibling, and the other due to infection, since the individual had Japanese B encephalitis at age 4 years.