In the assessment of health risks after nuclear accidents, some health consequences require special attention. For example, in their 2013 report on health risk assessment after the Fukushima nuclear accident, the World Health Organisation (WHO) panel of experts considered risks of breast cancer, thyroid cancer and leukaemia. For these specific cancer types, use was made of already published excess relative risk (ERR) and excess absolute risk (EAR) models for radiation-related cancer incidence fitted to the epidemiological data from the Japanese A-bomb Life Span Study (LSS). However, it was also considered important to assess all other types of solid cancer together and the WHO, in their above-mentioned report, stated "No model to calculate the risk for all other solid cancer excluding breast and thyroid cancer risks is available from the LSS data". Applying the LSS models for all solid cancers along with the models for the specific sites means that some cancers have an overlap in the risk evaluations. Thus, calculating the total solid cancer risk plus the breast cancer risk plus the thyroid cancer risk can overestimate the total risk by several per cent. Therefore, the purpose of this paper was to publish the required models for all other solid cancers, i.e. all solid cancers other than those types of cancer requiring special attention after a nuclear accident. The new models presented here have been fitted to the same LSS data set from which the risks provided by the WHO were derived. Although it is known already that the EAR and ERR effect modifications by sex are statistically significant for the outcome "all solid cancer", it is shown here that sex modification is not statistically significant for the outcome "all solid cancer other than thyroid and breast cancer". It is also shown here that the sex-averaged solid cancer risks with and without the sex modification are very similar once breast and thyroid cancers are factored out. Some other notable model differences between those already published for all solid cancers and those presented here for all other solid cancers are also given here. The models presented here can be used to improve on the methodology adopted by WHO after Fukushima and could contribute to emergency preparedness for future nuclear accidents.