The addition of hydrogen peroxide and steam to a hydrogen-fuelled HCCI engine was investigated at various fuel lean conditions (Phi(ef f) = 0.2-0.6) and compression ratios (15-20) using a 0-dimensional numerical model. The use of hydrogen peroxide as an ignition promoter demonstrated increased IMEP (16%-39%), thermal efficiency (up to 2%), and reduced NOx (50%-76%) when compared to the conventional method of intake charge heating. When hydrogen peroxide was used as an ignition promoter, a 15% addition of steam was sufficient to reduce NOx by 93%-97%, though this reduced IMEP and thermal efficiency slightly. When heat transfer was considered and steam addition was increased from 0%-10%, no increase in intake air heating was able to match the IMEP of 5% hydrogen peroxide addition without an increase in the equivalence ratio (up to 40%). The parametric space of hydrogen peroxide (0%-25%) and steam (0%-40%) addition was explored in view of engine performance metrics, showing the complete range of conditions possible through control of both inputs. A three-order reduction in NOx was possible through steam addition. An optimal balance of performance and emissions occurred at 5%-10% hydrogen peroxide and 10%-15% steam addition. In a study of compression ratio, very little hydrogen peroxide addition (< 5%) was required to achieve 98% of the maximum efficiency at higher compression ratios (19-20), though at lower compression ratios (< 17) impractical quantities of hydrogen peroxide were required. The 10% steam addition present at these conditions led to extremely low NOx levels for Phi(ef f) of 0.3 and 0.4, though at Phi(ef f) of 0.5 NOx levels would require some after-treatment. Maintaining constant a high or low load across steam additions was possible through reasonable adjustment of hydrogen peroxide addition.