The lambda-dynamics simulation method was used to study the binding of 10 five-member ring heterocycle derivatives to an artificial cavity created inside cytochrome C peroxidase by mutagenesis. Application of lambda dynamics using a multiple topology approach resulted in trapping in local minima. To extend the method to these cases, a new restraining potential was devised and added to the extended Hamiltonian. Two approximations were introduced in order to estimate the binding free energy within small simulation times using this potential: (a) The entropy terms related to the restraining potential are assumed to cancel, due to the similarity of the ligands. (b) The restraining potential calculated from the coordinates of the environmental atoms during a lambda-dynamics simulation is assumed to be equal to that of the average coordinates. Relatively short lambda-dynamics simulations with this restraining potential successfully yielded reasonable estimates of the binding affinity of the ligands as compared with both experimental data and free energy perturbation calculations. Long time lambda-dynamics simulations with a ten-ligand system revealed that better ligands tend to have small statistical errors, which is appropriate for screening out the plausible ligands from all candidates. Furthermore, short time lambda-dynamics simulations with ten identical ligands demonstrated that sufficient precision was achieved for putative discovery of tight binding ligands or guests.