Control of the timing and magnitude of heat release is one of the biggest challenges for premixed compression ignition, especially when attempting to operate at high load. Single-fuel strategies such as partially premixed combustion (PPC) use direct injection of gasoline to stratify equivalence ratio and retard heat release, thereby reducing pressure rise rate and enabling high load operation. However, retarding the heat release also reduces the maximum work extraction, effectively creating a tradeoff between efficiency and noise. Dual-fuel strategies such as reactivity controlled compression ignition (RCCI) use premixed gasoline and direct injection of diesel to stratify both equivalence ratio and fuel reactivity, which allows for greater control over the timing and duration of heat release. This enables combustion phasing closer to top dead center (TDC), which is thermodynamically favorable. However, the main control mechanism in RCCI is the ratio of the two fuels, and the diesel fraction typically reaches zero before full load is achieved. We propose a new strategy that effectively combines the benefits of RCCI and PPC by injecting both gasoline and diesel directly, enabling control over the in-cylinder distribution of both fuels. We present a comparison of RCCI, PPC, and our new strategy, direct dual fuel stratification (DDFS) at a nominal gross mean effective pressure of 0.9 MPa. DDFS allowed for combustion phasing near TDC with reduced combustion noise. Cyclic combustion instability was reduced significantly with the new strategy and approached levels typical of conventional diesel combustion. Compared to RCCI, there was a reduction in noise and required exhaust gas recirculation (EGR) while maintaining similar efficiency. Compared to PPC, there was a reduction in noise and an increase in efficiency. The new strategy therefore combines the efficiency advantage of RCCI with the load advantage of PPC, while reducing EGR and combustion instability.