Basic engine thermodynamics predicts that spark ignited engine efficiency is a function of both the compression ratio of the engine and the specific heat ratio of the working fluid. In practice the compression ratio of the engine is often limited due to knock. Both higher specific heat ratio and higher compression ratio lead to higher end gas temperatures and increase the likelihood of knock. When the knock limit is not reached, increased heat transfer losses at higher compression ratios can limit efficiency. In this paper, we investigate the role of both the compression ratio and the specific heat ratio on engine efficiency by conducting experiments comparing operation of a single-cylinder variable-compression ratio engine with both hydrogen–air and hydrogen–oxygen–argon mixtures. For low load operation, it is found that the hydrogen–oxygen–argon mixtures result in higher indicated thermal efficiencies. Peak efficiency for the hydrogen–oxygen–argon mixtures is found at compression ratio 5.5, whereas for the hydrogen–air mixture with an equivalence ratio of 0.24 the peak efficiency is found at compression ratio 13. The spark timing when operating the engine with hydrogen–oxygen–argon was found to be knock limited for compression ratios above 4.5. However, for operation with hydrogen–air the spark timing was not limited by knock. We apply a three-zone model to help explain the effects of specific heat ratio and compression ratio on efficiency. Operation with hydrogen–oxygen–argon mixtures at low loads is more efficient because the lower compression ratio results in a substantially larger portion of the gas residing in the adiabatic core rather than in the boundary layer and crevices, leading to less heat transfer and more complete combustion.