It has generally been assumed that the neutron and γ-ray absorbed doses in the data from the life span study (LSS) of the Japanese A-bomb survivors are too highly correlated for an independent separation of the all solid cancer risks due to neutrons and due to γ-rays. However, with the release of the most recent data for all solid cancer incidence and the increased statistical power over previous datasets, it is instructive to consider alternatives to the usual approaches. Simple excess relative risk (ERR) models for radiation-induced solid cancer incidence fitted to the LSS epidemiological data have been applied with neutron and γ-ray absorbed doses as separate explanatory covariables. A simple evaluation of the degree of independent effects from γ-ray and neutron absorbed doses on the all solid cancer risk with the hierarchical partitioning (HP) technique is presented here. The degree of multi-collinearity between the γ-ray and neutron absorbed doses has also been considered. The results show that, whereas the partial correlation between the neutron and γ-ray colon absorbed doses may be considered to be high at 0.74, this value is just below the level beyond which remedial action, such as adding the doses together, is usually recommended. The resulting variance inflation factor is 2.2. Applying HP indicates that just under half of the drop in deviance resulting from adding the γ-ray and neutron absorbed doses to the baseline risk model comes from the joint effects of the neutrons and γ-rays-leaving a substantial proportion of this deviance drop accounted for by individual effects of the neutrons and γ-rays. The average ERR/Gy γ-ray absorbed dose and the ERR/Gy neutron absorbed dose that have been obtained here directly for the first time, agree well with previous indirect estimates. The average relative biological effectiveness (RBE) of neutrons relative to γ-rays, calculated directly from fit parameters to the all solid cancer ERR model with both colon absorbed dose covariables, is 65 (95 %CI: 11; 170). Therefore, although the 95 % CI is quite wide, reference to the colon doses with a neutron weighting of 10 may not be optimal as the basis for the determination of all solid cancer risks. Further investigations into the neutron RBE are required, ideally based on the LSS data with organ-specific neutron and γ-ray absorbed doses for all organs rather than the RBE weighted absorbed doses currently provided. The HP method is also suggested for use in other epidemiological cohort analyses that involve correlated explanatory covariables.