An occlusion device for occluding a left atrial appendage, the occlusion device for use with a delivery system including a sheath, the occlusion device comprising: a compliant balloon defining a fluid-tight balloon chamber; an actuating shaft, which is (a) disposed at least partially within the balloon chamber, (b) connected to a distal end portion of the balloon, and (c) longitudinally moveable with respect to a proximal end portion of the balloon so as to set a distance between the distal and the proximal end portions (236, 238) of the balloon; and a locking mechanism, which is configured to assume locked and unlocked states, and which is configured, when in the locked state, to maintain, between the distal end portion of the balloon and the proximal end portion of the balloon, the distance set using the actuating shaft, characterized in that the occlusion device further comprises: a proximal LAA-orifice cover, which (a) is configured to assume a radially-compressed state when releasably disposed in the sheath, (b) comprises (i) a frame comprising a super-elastic metal, which causes the proximal LAA-orifice cover to automatically transition to a radially-expanded state upon release from the sheath, (ii) and a covering fixed to the frame, and (c) when in the radially-expanded state, is generally orthogonal to the actuating shaft and has a greatest dimension, measured perpendicular to the actuating shaft, of between 10 and 50 mm; and an orifice-support stent, which (a) is fixed to and extends distally from the proximal LAA-orifice cover, (b) is configured to assume a radially-compressed state and a radially-expanded state, and (c) is generally cylindrical when in the radially-expanded state, wherein the occlusion device is configured such that inflation of the balloon chamber transitions the orifice-support stent from its radially-compressed state to its radially-expanded state. a compliant balloon defining a fluid-tight balloon chamber; an actuating shaft, which is (a) disposed at least partially within the balloon chamber, (b) connected to a distal end portion of the balloon, and (c) longitudinally moveable with respect to a proximal end portion of the balloon so as to set a distance between the distal and the proximal end portions (236, 238) of the balloon; and a locking mechanism, which is configured to assume locked and unlocked states, and which is configured, when in the locked state, to maintain, between the distal end portion of the balloon and the proximal end portion of the balloon, the distance set using the actuating shaft, characterized in that the occlusion device further comprises: a proximal LAA-orifice cover, which (a) is configured to assume a radially-compressed state when releasably disposed in the sheath, (b) comprises (i) a frame comprising a super-elastic metal, which causes the proximal LAA-orifice cover to automatically transition to a radially-expanded state upon release from the sheath, (ii) and a covering fixed to the frame, and (c) when in the radially-expanded state, is generally orthogonal to the actuating shaft and has a greatest dimension, measured perpendicular to the actuating shaft, of between 10 and 50 mm; and an orifice-support stent, which (a) is fixed to and extends distally from the proximal LAA-orifice cover, (b) is configured to assume a radially-compressed state and a radially-expanded state, and (c) is generally cylindrical when in the radially-expanded state, wherein the occlusion device is configured such that inflation of the balloon chamber transitions the orifice-support stent from its radially-compressed state to its radially-expanded state. a proximal LAA-orifice cover, which (a) is configured to assume a radially-compressed state when releasably disposed in the sheath, (b) comprises (i) a frame comprising a super-elastic metal, which causes the proximal LAA-orifice cover to automatically transition to a radially-expanded state upon release from the sheath, (ii) and a covering fixed to the frame, and (c) when in the radially-expanded state, is generally orthogonal to the actuating shaft and has a greatest dimension, measured perpendicular to the actuating shaft, of between 10 and 50 mm; and an orifice-support stent, which (a) is fixed to and extends distally from the proximal LAA-orifice cover, (b) is configured to assume a radially-compressed state and a radially-expanded state, and (c) is generally cylindrical when in the radially-expanded state, wherein the occlusion device is configured such that inflation of the balloon chamber transitions the orifice-support stent from its radially-compressed state to its radially-expanded state.