Ultra-high efficiency combustion of hydrogen-in-oxygen, comparable with fuel cell efficiency, can be achieved by using Argon rather than atmospheric Nitrogen as a working fluid. Otto-cycle thermal efficiency is influenced by compression ratio and the ratio of specific heats. The use of Argon as a working fluid increases the specific heat ratio, allowing for higher achievable thermal efficiency. Previous research has identified that the undesirable side-effect of using Argon, however, is that engine knocking occurs more readily. As a result, gains in efficiency are yet to be realized because the compression ratio is reduced to avoid knocking. The purpose of this study is the numerical determination of whether engine knocking in H2-O2-Ar HCCI combustion can be mitigated using reduced equivalence ratios, and delayed combustion timing allowing for higher compression ratios and thereby higher thermal efficiency. The results show that the relationship between indicated efficiency and compression ratio is parabolic, and there is a maximum point beyond which further increases in compression ratio actually decrease efficiency. The study also explores the effects of other parameters such as combustion timing, boost pressure, equivalence ratio and %Argon upon indicated efficiency. The results identify the maximum indicated efficiency point surpassing 48% can be achieved using a compression ratio of 11, intake pressure of 2.0 atm, Argon fraction of 80% and highly delayed combustion timings.