Background/objective: Many occupational exposures causing disease cannot feasibly be eliminated entirely, but policies that reduce the exposures may be under consideration. This paper sets out to clarify how to estimate the reduction in occupational disease following a reduction in exposure, and shows a real-data illustration for doing this. Methods: Modest extensions of standard expressions for attributable fractions permit estimation of fractions by which cases would be reduced by policies that do not eliminate exposure but change exposure distributions. However, this requires information on the exposure-response relation and on distribution of exposures. Results: From hypothetical scenarios and a real example this paper explores how attributable cases are distributed by exposure level and, in particular, the proportion by which attributable cancers are reduced by eliminating exposures above a limit (the classic occupational limit regulation). It shows how this depends on the shape of the exposure-response relation and to some extent the shape of the exposure distribution, as well as on the proportion exposed above the limit. For linear no-threshold relations and left-skewed exposure distributions, the majority of the burden may be in a large number of people experiencing small relative risks, and thus may not be tackled by a strategy to reduce exposures above a certain limit. Conclusion: With appropriate data, estimating the disease burden in terms of the distribution of exposure is straightforward and can help to clarify the likely outcome of an intervention.