Context. High-resolution spectroscopy has recently revealed in many low-mass X-ray binaries hosting a neutron star that the shape of the broad iron line observed in the 6.4–6.97 keV range is consistently well-fitted by a relativistically smeared line profile. Aims. The presence of other broad features, besides the iron line, together with a high S/N of the spectra offer the possibility of testing a self-consistent approach to the overall broadband reflection spectrum and evaluating the impact of the reflection component in the formation of the broadband X-ray spectra. Methods. We analyzed two XMM-Newton observations of the bright atoll source 4U 1705-44, which can be considered a prototype of the class of the persis...