We analysed the X-ray spectra of six observations, simultaneously taken with XMM-Newton and Rossi X-ray Timing Explorer (RXTE), of the neutron-star low-mass X-ray binary 4U 1636-53. The observations cover several states of the source, and therefore a large range of inferred mass accretion rate. These six observations show a broad emission line in the spectrum at around 6.5 keV, likely due to iron. We fitted this line with a set of phenomenological models of a relativistically broadened line, plus a model that accounts for relativistically smeared and ionized reflection from the accretion disc. The latter model includes the incident emission from both the neutron-star surface or boundary layer and the corona that is responsible for the high-...