A blood vessel occlusion device configured to fully occlude a blood vessel in an unconstrained shape of the blood vessel occlusion device, the blood vessel occlusion device having a central longitudinal axis and comprising: (a) a hub, (b) a self-expanding support frame distally of the hub, the support frame comprising a plurality of wire segments forming a plurality of cells, said support frame being self-expandable from a constrained shape to the unconstrained shape that consists of (i) a substantially cylindrical portion having a diameter and an axis that is coincident with the central longitudinal axis, the substantially cylindrical portion having a variation in diameter of 25% or less along the axial length of the substantially cylindrical portion, said substantially cylindrical portion consisting of a first ring of said cells extending in a 360° rotation around the central longitudinal axis and a second ring of said cells extending distally of the first ring in a 360° rotation around the central longitudinal axis, and (ii) a substantially conic transition portion disposed between the substantially cylindrical portion and the hub, and (c) a covering material covering cells within the transition portion characterized in that the covering material covers as well a portion of each cell in the first ring of the substantially cylindrical portion while leaving at least a portion of the wire segments in the first ring and the second ring exposed. (a) a hub, (b) a self-expanding support frame distally of the hub, the support frame comprising a plurality of wire segments forming a plurality of cells, said support frame being self-expandable from a constrained shape to the unconstrained shape that consists of (i) a substantially cylindrical portion having a diameter and an axis that is coincident with the central longitudinal axis, the substantially cylindrical portion having a variation in diameter of 25% or less along the axial length of the substantially cylindrical portion, said substantially cylindrical portion consisting of a first ring of said cells extending in a 360° rotation around the central longitudinal axis and a second ring of said cells extending distally of the first ring in a 360° rotation around the central longitudinal axis, and (ii) a substantially conic transition portion disposed between the substantially cylindrical portion and the hub, and (i) a substantially cylindrical portion having a diameter and an axis that is coincident with the central longitudinal axis, the substantially cylindrical portion having a variation in diameter of 25% or less along the axial length of the substantially cylindrical portion, said substantially cylindrical portion consisting of a first ring of said cells extending in a 360° rotation around the central longitudinal axis and a second ring of said cells extending distally of the first ring in a 360° rotation around the central longitudinal axis, and (ii) a substantially conic transition portion disposed between the substantially cylindrical portion and the hub, and (c) a covering material covering cells within the transition portion characterized in that the covering material covers as well a portion of each cell in the first ring of the substantially cylindrical portion while leaving at least a portion of the wire segments in the first ring and the second ring exposed.