System for covering a motor-vehicle luggage compartment, said system comprising two lateral panels lining said compartment and a luggage cover, said luggage cover comprising: • a casing provided with a transverse slot, with two lateral end pieces mounted at the ends of said casing and with a winding shaft the ends of which are mounted for rotation on said end pieces on a transverse axis, said shaft being actuated in rotation in a winding direction by a spring means, said end pieces being provided with reversible locking means cooperating with respective reciprocal means provided at the front part of said panels, said means and reciprocal means being arranged so that they can be made to cooperate by positioning of said luggage cover with said end pieces put in offset angular position, according said axis, with respect to the nominal angular position that they occupy when said luggage cover is mounted on said panels, the rotation of said end pieces in said nominal position activating said locking means, • a curtain passing through said slot and having a front edge associated with said shaft so as to be able to be wound around under the action of said spring means in order to pass reversibly from an unwound configuration of covering the luggage to a wound configuration of access to the luggage, • a crossmember for stiffening a rear edge of said curtain, said crossmember being provided with two transverse fingers projecting laterally and being able to cooperate with reception means provided at the rear of said panels to hold said curtain in the unwound configuration, said system being characterised in that: • said end pieces are each provided with a housing accommodating a respective finger when said curtain is brought into the wound configuration, • said fingers and housings are arranged so as to constrain them to rotate with each other, so that the rotational actuation of said crossmember on said axis when said curtain is in the wound configuration causes a positioning of said end pieces in an offset angular position allowing removal of said luggage cover from said panels. • a casing provided with a transverse slot, with two lateral end pieces mounted at the ends of said casing and with a winding shaft the ends of which are mounted for rotation on said end pieces on a transverse axis, said shaft being actuated in rotation in a winding direction by a spring means, said end pieces being provided with reversible locking means cooperating with respective reciprocal means provided at the front part of said panels, said means and reciprocal means being arranged so that they can be made to cooperate by positioning of said luggage cover with said end pieces put in offset angular position, according said axis, with respect to the nominal angular position that they occupy when said luggage cover is mounted on said panels, the rotation of said end pieces in said nominal position activating said locking means, • a curtain passing through said slot and having a front edge associated with said shaft so as to be able to be wound around under the action of said spring means in order to pass reversibly from an unwound configuration of covering the luggage to a wound configuration of access to the luggage, • a crossmember for stiffening a rear edge of said curtain, said crossmember being provided with two transverse fingers projecting laterally and being able to cooperate with reception means provided at the rear of said panels to hold said curtain in the unwound configuration, • said end pieces are each provided with a housing accommodating a respective finger when said curtain is brought into the wound configuration, • said fingers and housings are arranged so as to constrain them to rotate with each other, so that the rotational actuation of said crossmember on said axis when said curtain is in the wound configuration causes a positioning of said end pieces in an offset angular position allowing removal of said luggage cover from said panels.