An intravascular device configured to treat an aneurysm that includes a support structure including metal struts configured to be positioned in a body lumen and defining a central fluid passage that extends axially along the support structure, and a knitted mesh cover disposed over an exterior thereof and across a radial arc and along a length of the support structure sufficient to exceed an opening of an aneurysm to be treated, and the cover includes a polymer fiber having a diameter of at least 40 nanometers to 30 microns and apertures therethrough, the apertures being sized to prevent blood from passing through the device to prevent further expansion of the aneurysm. Devices including apertures that are at least 20 microns and sized to minimize or prevent an aneurysm-filling material from exiting the aneurysm through the knitted mesh cover and support structure, and methods of stenting, are also encompassed.