Low profile, self-expandable, blood flow restrictors include a hollow channel open at axial ends to allow blood flow through the restrictor installed in a blood vessel. The channel may include a mesh and have a narrowing, or sandglass, profile to reduce blood flow. The sandglass shape is in a central portion of the channel and may be surrounded by a blocking coating impermeable to blood flow or a suture that dissolves over time. The mesh may be formed of a memory alloy. Restrictors include a retrieval connector at an end that is permeable to blood flow and permits attachment for restrictor positioning with a catheter.