Context : Aims : We derive simple estimates of the maximum efficiency with which matter can be ejected by the propeller mechanism in disk-fed , rotating magnetic neutron stars . Some binary evolution scenarios envisage that this mechanism is responsible for expelling to infinity the mass inflowing at a low rate from the companion star , therefore limiting the total amount of mass that can be accreted by the neutron star . Methods : We demonstrate that , for typical neutron star parameters , a maximum of \eta _ { pro } < 5.7 ( P _ { -3 } ) ^ { 1 / 3 } times more matter than accreted can be expelled through the propeller mechanism at the expenses of the neutron star rotational energy ( P _ { -3 } is the NS spin period in unit of 10 ^ { -3 } s ) . Approaching this value , however , would require a great deal of fine tuning in the system parameters and the properties of the interaction of matter and magnetic field at the magnetospheric boundary . Results : We conclude that some other mechanism must be invoked in order to prevent that too much mass accretes onto the neutron stars of some low mass X-ray binaries . Conclusions :