A non-occlusive device is provided that includes a coilable section and a docking section. When deployed from a microcatheter within a wide-neck vascular aneurysm, the coilable section is configured to become coiled into a coil defining a sequence of concentric loops, and to bridge a neck of the aneurysm so as to at least partially cover an orifice of the aneurysm, when in use. The docking section is configured to be deployed from the microcatheter within the aneurysm. The docking section extends distally from an outermost one of the concentric loops of the coil, and is shaped so as to define one or more concentric loops having an outer diameter less than an outer diameter of the concentric loops of the coil. The docking section is configured to anchor, stabilize, and/or assist with positioning of the device within the aneurysm. Other embodiments are also described.