The impact of compression ratio on engine efficiency is well known. A plethora of mechanical concepts have been proposed for altering engine compression ratio in real time. Some of these, like free-piston configurations or complex crank-slider mechanisms have the added ability to alter piston trajectory along with compression ratio. This secondary modality raises the question: Is there a more optimal piston position versus crank-angle profile for spark-ignition (SI) engines than the near-sinusoidal motion produced by a traditional four-bar crank-slider mechanism? Very little published literature directly addresses this question. This work presents the results of a quasi-dimensional SI engine model using piston trajectory as an input. Specific trajectory traits including increased dwell at top dead center and asymmetric compression and expansion strokes were swept. The trajectory also was optimized using a single objective genetic algorithm with 60 individuals and 40 generations. Results of the study show that increasing TDC dwell compared to a traditional volume profile increases efficiency by retarding start of ignition well into the dwell region. Asymmetric profiles can enhance indicated efficiency by a greater amount though increased piston speeds during compression may have greater friction, an aspect not considered by the model. The genetic algorithm results show that the thermodynamically optimum piston trajectory can enhance indicated efficiency by approximately 14.6 percent over the baseline sinusoidal profile. Our findings indicate that optimizing piston trajectory may significantly improve engine thermal efficiency and that additional research is warranted to more accurately quantify potential gains.