The present invention relates to an apparatus and method for stretch wrapping a load in an efficient manner so as to tightly and securely wrap the load at a desired tension without rupturing the packaging material. The method and apparatus compensate for variation in demand rate as the load is wrapped so as to apply the wrapping material to a load at a desired force, maintain the desired containment tension on the wrapping material on the load after wrapping, and prevent the wrapping material from rupturing during wrapping. The apparatus combines two systems, power assisted roller stretch (“PRS”) and roller stretch (“RS”) to vary the supply rate of the packaging material as the demand rate varies. The apparatus automatically switches between the two types of prestretch to achieve “high” and “low” wrapping force dependent upon the demand rate. Changes in the demand rate are sensed by monitoring changes in the payoff angle of the packaging material extending between the dispenser and the load.