Apparatus for use with a native valve of a heart of the subject, the native valve having an annulus and native leaflets, and being disposed between an atrium of the heart and a ventricle of the heart, the apparatus comprising: a sheath, percutaneously advanceable to the native valve; and a prosthetic valve: comprising an expandable frame, a plurality of prosthetic leaflets disposed within the expandable frame, and a plurality of protrusions, having: a collapsed state for percutaneous delivery to the native valve via the sheath, and a tendency to expand toward the expanded state, characterized in that: the apparatus further comprises a prosthetic valve support: having a collapsed state for percutaneous delivery to the native valve via the sheath, and comprising an annular element, configured to be placed at the native valve such that the annular element is positioned along the annulus and defines an inner cross-sectional area; and the prosthetic valve: has an expanded state in which the prosthetic valve has a cross-sectional area that is greater than the inner cross-sectional area of the prosthetic valve support; and is configured, subsequently to the placement of the prosthetic valve support: to be partially deployed, to be subsequently moved upstream with respect to the prosthetic valve support so as to sandwich the native leaflets between the protrusions and the prosthetic valve support, and to be subsequently deployed into the expanded state such that a tendency of the prosthetic valve to expand holds the prosthetic valve in place with respect to the prosthetic valve support. a sheath, percutaneously advanceable to the native valve; and a prosthetic valve: comprising an expandable frame, a plurality of prosthetic leaflets disposed within the expandable frame, and a plurality of protrusions, having: a collapsed state for percutaneous delivery to the native valve via the sheath, and a tendency to expand toward the expanded state, characterized in that: comprising an expandable frame, a plurality of prosthetic leaflets disposed within the expandable frame, and a plurality of protrusions, having: a collapsed state for percutaneous delivery to the native valve via the sheath, and a tendency to expand toward the expanded state, characterized in that: a collapsed state for percutaneous delivery to the native valve via the sheath, and a tendency to expand toward the expanded state, characterized in that: the apparatus further comprises a prosthetic valve support: having a collapsed state for percutaneous delivery to the native valve via the sheath, and comprising an annular element, configured to be placed at the native valve such that the annular element is positioned along the annulus and defines an inner cross-sectional area; and having a collapsed state for percutaneous delivery to the native valve via the sheath, and comprising an annular element, configured to be placed at the native valve such that the annular element is positioned along the annulus and defines an inner cross-sectional area; and the prosthetic valve: has an expanded state in which the prosthetic valve has a cross-sectional area that is greater than the inner cross-sectional area of the prosthetic valve support; and is configured, subsequently to the placement of the prosthetic valve support: to be partially deployed, to be subsequently moved upstream with respect to the prosthetic valve support so as to sandwich the native leaflets between the protrusions and the prosthetic valve support, and to be subsequently deployed into the expanded state such that a tendency of the prosthetic valve to expand holds the prosthetic valve in place with respect to the prosthetic valve support. to be partially deployed, to be subsequently moved upstream with respect to the prosthetic valve support so as to sandwich the native leaflets between the protrusions and the prosthetic valve support, and to be subsequently deployed into the expanded state such that a tendency of the prosthetic valve to expand holds the prosthetic valve in place with respect to the prosthetic valve support.