Gasoline partially premixed combustion (PPC) has the potential of high efficiency and simultaneous low soot and NOx emissions. Running the engine in PPC mode with high octane number fuels has the advantage of a longer premix period of fuel and air which reduces soot emissions. The problem is the ignitability at low load and idle operating conditions. In a previous study it was shown that it is possible to use NVO to improve combustion stability and combustion efficiency at operating conditions where available boosted air is assumed to be limited. NVO has the disadvantage of low net indicated efficiency due to heat losses from recompressions of the hot residual gases. An alternative to NVO is the rebreathing valve strategy where the exhaust valves are reopened during the intake stroke. The net indicated efficiency is expected to be higher with the rebreathing strategy but the question is if similar improvements in combustion stability can be achieved with rebreathing as with NVO. The results show that the rebreathing valve strategy has similar improvements on combustion stability as NVO when the same fuel injection strategy is used. This work also includes results with the NVO valve strategy where a fuel injection is added during the NVO. When a fuel injection is added during the NVO, an additional improvement on combustion stability can be seen which is unmatched by the rebreathing valve strategy.