An assembly for implanting a balloon-expandable prosthetic aortic valve in a patient's body, the assembly comprising: a delivery apparatus comprising an elongated shaft having an inflatable balloon, and a radially expandable prosthetic aortic valve adapted to be mounted on the shaft in a radially collapsed configuration for delivery into the body, the prosthetic aortic valve comprising: a balloon-expandable annular frame made of a nickel-cobalt-chromium alloy and comprising a plurality of angularly spaced commissure windows each comprising an enclosed opening between first and second axially oriented side struts; a leaflet structure positioned within the frame and comprising a plurality of leaflets each comprising two opposing primary side tabs, each primary side tab being paired with an adjacent primary side tab of an adjacent leaflet to form commissures of the leaflet structure, each pair of primary side tabs extending radially outwardly through a corresponding commissure window to a location outside of the frame, the portions of the primary side tabs located outside of the frame extend circumferentially away from one another and along an exterior surface of the side struts; and a plurality of wedges, each wedge being positioned between the side struts of a commissure window and separating the pair of primary side tabs extending through the commissure window, the wedge being urged radially inwardly against the primary side tabs, characterized in that each wedge is sutured to a flexible reinforcing sheet that is also sutured to each of the pair of primary side tabs. a delivery apparatus comprising an elongated shaft having an inflatable balloon, and a radially expandable prosthetic aortic valve adapted to be mounted on the shaft in a radially collapsed configuration for delivery into the body, the prosthetic aortic valve comprising: a balloon-expandable annular frame made of a nickel-cobalt-chromium alloy and comprising a plurality of angularly spaced commissure windows each comprising an enclosed opening between first and second axially oriented side struts; a leaflet structure positioned within the frame and comprising a plurality of leaflets each comprising two opposing primary side tabs, each primary side tab being paired with an adjacent primary side tab of an adjacent leaflet to form commissures of the leaflet structure, each pair of primary side tabs extending radially outwardly through a corresponding commissure window to a location outside of the frame, the portions of the primary side tabs located outside of the frame extend circumferentially away from one another and along an exterior surface of the side struts; and a plurality of wedges, each wedge being positioned between the side struts of a commissure window and separating the pair of primary side tabs extending through the commissure window, the wedge being urged radially inwardly against the primary side tabs, characterized in that each wedge is sutured to a flexible reinforcing sheet that is also sutured to each of the pair of primary side tabs. a balloon-expandable annular frame made of a nickel-cobalt-chromium alloy and comprising a plurality of angularly spaced commissure windows each comprising an enclosed opening between first and second axially oriented side struts; a leaflet structure positioned within the frame and comprising a plurality of leaflets each comprising two opposing primary side tabs, each primary side tab being paired with an adjacent primary side tab of an adjacent leaflet to form commissures of the leaflet structure, each pair of primary side tabs extending radially outwardly through a corresponding commissure window to a location outside of the frame, the portions of the primary side tabs located outside of the frame extend circumferentially away from one another and along an exterior surface of the side struts; and a plurality of wedges, each wedge being positioned between the side struts of a commissure window and separating the pair of primary side tabs extending through the commissure window, the wedge being urged radially inwardly against the primary side tabs, characterized in that each wedge is sutured to a flexible reinforcing sheet that is also sutured to each of the pair of primary side tabs.