A flow reducing implant for reducing blood flow in a blood vessel having a cross sectional dimension, the flow reducing implant comprising a hollow element adapted for placement in the blood vessel defining a flow passage therethrough, said flow passage comprising at least two sections, one with a larger diameter and one with a smaller diameter, wherein said smaller diameter is smaller than a cross section of the blood vessel. A plurality of tabs anchor, generally parallel to the blood vessel wall, are provided in some embodiments of the invention.
