The Burton et al. equation and the Ring Current Atmosphere Interaction Model (RAM) code give about equally good fits to Dst profiles of strong magnetic storms, yet they are driven by different functions of the interplanetary electric field, one rising linearly and the other eventually saturating. We show that by reformulating the Burton et al. equation such that a quadratic form of the driving term replaces the original linear form, the new prediction algorithm driven by the saturation form of the driving electric field produces about equally good fits to Dst as the original Burton et al. equation and the RAM code. The form of the quadratic driving term is constructed by specializing a general form given by dimensional analysis.