Several groups have considered the option of using multiple-energy window emission data to improve reconstruction accuracy for PET/MR imaging. However, the feasibility of this approach has only been studied with analytic simulations. To be able to handle realistic measurements a remaining challenge is related to the detection efficiencies (“normalisation”) for the different energy windows, which likely differ for scattered and unscattered events given the heterogeneity of photon energies, angles of incidence, and points of origination. In addition, the lower energy windows will potentially contain events that have been affected by scatter in the detector. This manuscript investigates the problem of estimating the normalisation factors for PET data acquired from multiple energy windows.