A cardiac implant for implantation around an exterior of a heart, the implant comprising: an implant body comprising a mesh material that is formed into a generally tubular configuration, the implant body comprising a leading end portion defining an open leading end and a trailing end portion defining an open trailing end of a diameter that is less than a diameter of the open leading end, the trailing end portion having a length configured to extend proximal of the apex of the heart when the leading end portion is positioned in an atrial-ventricular groove of the heart; and a fillable bladder mounted to the implant body and positioned relative to the open leading end such that, when the leading end portion is positioned in the atrial-ventricular groove, the fillable bladder is positionable on an exterior of a heart wall adjacent a mitral valve to provide localized pressure to an annulus of the mitral valve to bring leaflets of the mitral valve into closer proximity with one another, wherein the fillable bladder comprises: an inner bladder layer positioned with respect to the mesh material of the implant body to face inwardly toward the exterior of the heart wall when the leading end portion is positioned in the atrial-ventricular groove of the heart, and an outer bladder layer positioned opposite from the inner bladder layer , wherein the inner bladder layer has a compliance that is greater than a compliance of the outer bladder layer such that, when implanted and inflated, the bladder expands more inwardly toward the heart wall than outwardly from the heart wall. an implant body comprising a mesh material that is formed into a generally tubular configuration, the implant body comprising a leading end portion defining an open leading end and a trailing end portion defining an open trailing end of a diameter that is less than a diameter of the open leading end, the trailing end portion having a length configured to extend proximal of the apex of the heart when the leading end portion is positioned in an atrial-ventricular groove of the heart; and a fillable bladder mounted to the implant body and positioned relative to the open leading end such that, when the leading end portion is positioned in the atrial-ventricular groove, the fillable bladder is positionable on an exterior of a heart wall adjacent a mitral valve to provide localized pressure to an annulus of the mitral valve to bring leaflets of the mitral valve into closer proximity with one another, wherein the fillable bladder comprises: an inner bladder layer positioned with respect to the mesh material of the implant body to face inwardly toward the exterior of the heart wall when the leading end portion is positioned in the atrial-ventricular groove of the heart, and an outer bladder layer positioned opposite from the inner bladder layer , wherein the inner bladder layer has a compliance that is greater than a compliance of the outer bladder layer such that, when implanted and inflated, the bladder expands more inwardly toward the heart wall than outwardly from the heart wall. an inner bladder layer positioned with respect to the mesh material of the implant body to face inwardly toward the exterior of the heart wall when the leading end portion is positioned in the atrial-ventricular groove of the heart, and an outer bladder layer positioned opposite from the inner bladder layer , wherein the inner bladder layer has a compliance that is greater than a compliance of the outer bladder layer such that, when implanted and inflated, the bladder expands more inwardly toward the heart wall than outwardly from the heart wall. <EOS>