In an electrically conductive lead adapted for implantation in a human or animal body, and a method for making such a lead, a drug-dispensing member is disposed at a distal end portion of the lead, at which an electrode member is disposed that is adapted to emit and/or sense electrical signals associated with medical therapy. The drug-dispensing member has a configuration so that, after implantation, the amount of drug released into the body per time unit is automatically controlled to smoothly vary with time from al larger amount to a smaller amount in accordance with a predetermined relationship of the amount of drug released as a function of time.