An assembly includes a medical implantable lead adapted to be attached with a distal end of the lead to an organ inside a human or animal body, the medical implantable lead being formed with an inner lumen extending along essentially the entire length of the lead. The assembly also includes a support core that has a desirable stiffness and a suitably cross sectional dimension such that it is insertable into the lumen (7) in order to increase the stiffness of the lead along its length during its working life when being implanted into a body. A method for implanting a medical implantable lead into a human or animal body makes use of such an assembly.