Mid-power rocketry is considered the next step from model rocketry. Rockets in this class are typically powered by a "D" or larger engine and weigh more than 1 pound, but less than 3.3 pounds. Large clusters of black powder motors may also fall into the mid-power class. Usually a phone call (but not a full waiver) to your local FAA office is required for a launching a rocket in this size category.
An Apogee Rockets Saturn V kit is an excellent example of a scale model that falls into this category. The Aerotech Initiator is a great example of a beginner's kit for mid-power rocketry.