The aim of this study is to determine the conditions necessary to achieve optimum chest compression (CC) performance during constant peak displacement cardiopulmonary resuscitation (CPR). This was accomplished by first performing a sensitivity analysis on a theoretical constant peak displacement CPR CC model to identify the parameters with the highest sensitivity. Next, the most sensitive parameters were then optimized for net sternum-to-spine compression depth, using a two-variable non-linear least squares method. The theoretical CC model was found to be most sensitive to: thoracic stiffness, maximum sternal displacement, CC rate, and back support stiffness. Based on a two-variable, non-linear least squares analysis to optimize the model for the net sternum-to-spine compression depth during constant peak displacement CPR, it was found that the optimum ranges for the CC rate and back support stiffness are between 40–120 cpm and 241.0–1198.5 Ncm−1, respectively. Clinically, this suggests that current ERC guidelines for the CC rate during peak displacement CPR are appropriate; however, practitioners should be aware that the stiffness of the back support surfaces found in many hospitals may be sub-optimal and should consider using a backboard or a concrete floor to enhance CPR effectiveness.