While it is recognized that neutrons contributed to the excess cancer incidence and mortality among the atomic bomb survivors in Hiroshima, there is no possibility to deduce the magnitude of this contribution from the data. This remains true even if the neutron doses in the dosimetry system DS86 are corrected upwards in line with recent neutron activation measurements. In spite of this fact, important information can be obtained in the form of an inverse relation of the risk coefficients for gamma-rays and neutrons. Such an interrelation must apply because the observed excess incidence or mortality is made up of a gamma-ray and a neutron component; increased attribution to neutrons decreases the attribution to photons. Computations with the uncorrected and the corrected DS86 are performed for the mortality and the incidence of solid tumors combined. They refer to doses up to 2 Gy and employ the constant relative risk model and a linear-quadratic dose dependence with variable ratio-the neutron relative biological effectiveness (RBE) at low doses-of the linear component for neutrons and gamma-rays. In line with past analyses, no quadratic component is obtained with the uncorrected DS86. but it is seen, even in these calculations, that the assumption of increased neutron RBEs does not translate into proportional increases of the risk coefficients of neutrons, because it leads to substantially reduced risk estimates for gamma-rays. Calculations with the corrected dosimetry bring out this reciprocity even more clearly. High values of the neutron RBE reduce-in line with recent suggestions by Rossi and Zaider-the risk estimates for gamma-rays substantially. Even a purely quadratic dose relation for gamma-rays is consistent with the data; it requires no major increase of the nominal risk coefficients for neutrons over the currently assumed values. The cancer data from Hiroshima can still provide 'prudent' risk estimates for photons, but with the corrected DS86, they do not prove that there is a linear component in the dose dependence for photons.