A self-expandable occluding device can both cover the neck of an outpouching and serve as a permanent embolic plug thereby immediately stabilizing the outpouching. The self-expandable device effectively covers the neck of an outpouching with, for example, a mesh, or other at least partially occluding component, in a desired orientation across the neck of the outpouching without projecting into the
parent vessel. The device incorporates elements which immediately stabilize the device in the outpouching, in effect, functioning as a permanent embolic plug. An embolic disc is combined with retention arms of flexible material, which deploy within the outpouching and provide immediate stabilization thereby retaining the occluding component or mesh across the neck of the outpouching. In illustrative embodiments, the arms are in the form of coils configured to deploy into three dimensional structures.