A device for implantation within a vascular defect or aneurysm comprising: a self-expanding resilient outer layer having a proximal end, a distal end, a longitudinal axis; an inner layer of filamentary members disposed within the self-expanding resilient outer layer; the self-expanding resilient outer layer comprising a plurality of elongate filaments with a woven structure secured relative to each other at proximal ends and distal ends thereof, wherein the self-expanding resilient outer layer having a radially constrained elongated state configured for delivery within a microcatheter with the elongate filaments extending longitudinally from the proximal end of the self-expanding resilient outer layer to the distal end of the self-expanding resilient outer layer radially adjacent each other along a length of the elongate filaments, and the self-expanding resilient outer layer having an expanded relaxed state with a longitudinally shortened configuration relative to the radially constrained state with a major transverse diameter, the elongate filaments forming the self-expanding resilient outer layer in a smooth path radially expanded from the longitudinal axis between the proximal end of the self-expanding resilient outer layer and the distal end of the self-expanding resilient outer layer, and including a plurality of openings in the self-expanding resilient outer layer formed between the elongate filaments; characterized in that the plurality of elongate filaments comprises first filaments having a first transverse size and second filaments having a second transverse size, the first transverse size being larger than the second transverse size; the self-expanding resilient outer layer in an expanded state has a radial stiffness of about 0.062 N (0.014 lbf) to about 1.263 N (0.284 lbf) defined by the expression (1.2 X 10 6 lbf/D 4)(N l d l 4 + N s d s 4) where D is a diameter of the outer layer in the expanded state in inches, N l is the number of large filaments in the permeable shell, N s is the number of small filaments in the permeable shell, d l is the diameter of the largest filaments in inches, and d s is the diameter of the smallest filaments in inches; the inner layer has a distal-most surface defining a distal contour, the distal contour of the inner layer being the same as the distal contour of the self-expanding resilient outer layer at least in the expanded relaxed state, an internal gap being established between the distal-most surface of the self-expanding resilient outer layer and the distal-most surface of the inner layer in the expanded relaxed state, the internal gap being between 5% and 40% of a total longitudinal height of the device measured along a longitudinal axis of the device. a self-expanding resilient outer layer having a proximal end, a distal end, a longitudinal axis; an inner layer of filamentary members disposed within the self-expanding resilient outer layer; the self-expanding resilient outer layer comprising a plurality of elongate filaments with a woven structure secured relative to each other at proximal ends and distal ends thereof, wherein the self-expanding resilient outer layer having a radially constrained elongated state configured for delivery within a microcatheter with the elongate filaments extending longitudinally from the proximal end of the self-expanding resilient outer layer to the distal end of the self-expanding resilient outer layer radially adjacent each other along a length of the elongate filaments, and the self-expanding resilient outer layer having an expanded relaxed state with a longitudinally shortened configuration relative to the radially constrained state with a major transverse diameter, the elongate filaments forming the self-expanding resilient outer layer in a smooth path radially expanded from the longitudinal axis between the proximal end of the self-expanding resilient outer layer and the distal end of the self-expanding resilient outer layer, and including a plurality of openings in the self-expanding resilient outer layer formed between the elongate filaments;