So far it has not been explained convincingly how antifreeze peptides (AFP) prevent the growth of ice crystals. Step-pinning models as proposed by DeVries, Knight, and others imply a degree of permanent adsorption which it is difficult to reconcile with the observed concentration dependence of the hysteresis gap width. We propose a novel mechanism whereby the role of the antifreeze peptide is to increase the step energy (line tension) associated with the formation of 2D nuclei thereby reducing the nucleation temperature. This is achieved by fairly strong positive adsorption on the crystal faces with reduced adsorption close to a step leading to a negative line excess. The model predicts, in excellent agreement with experiment, a linear dependence of delta T on log(e) c where delta T is the freezing point lowering and c the peptide concentration. The magnitudes of the slopes lead to reasonable values of the negative line excess and to estimates of the peptide concentration at which the amount adsorbed should be significantly below the saturation level. They also lead to estimates of adsorption free energies for isolated molecules of order 10kT. These findings provide good circumstantial evidence that the proposed mechanism is at least partially correct. The concept of positive adsorption on crystal faces with negative adsorption close to steps may have important implications not just for AFP but for the general area of additive effects on crystal growth kinetics from melts.