Recent radiobiological studies have provided compelling evidence that the low energy X-rays as used in mammography are approximately four times--but possibly as much as six times--more effective in causing mutational damage than higher energy X-rays. Since current radiation risk estimates are based on the effects of high energy gamma radiation, this implies that the risks of radiation-induced breast cancers for mammography X-rays are underestimated by the same factor. The balance of risk and benefit for breast screening have been re-analysed for relative biological effectiveness (RBE) values between 1 and 6 for mammography X-rays. Also considered in the analysis is a change in the dose and dose-rate effectiveness factor (DDREF) from 2 to 1, women with larger than average breasts and implications for women with a family history of breast cancer. A potential increase in RBE to 6 and the adoption of a DDREF of unity does not have any impact on the breast screening programme for women aged 50-70 years screened on a 3 yearly basis. Situations for which breast screening is not justified due to the potential cancers induced relative to those detected (the detection-to-induction ratio (DIR)) are given for a range of RBE and DDREF values. It is concluded that great caution is needed if a programme of early regular screening with X-rays is to be used for women with a family history of breast cancer since DIR values are below 10 (the lowest value considered acceptable for women below 40 years) even for modest increases in the RBE for mammography X-rays.