There is significant motivation to extend the operating range of naturally aspirated HCCI combustion to high load (8-12 bar IMEP) to attain a combustion strategy with the efficiency benefits of HCCI but without the lost power density of a lean or highly diluted charge. Currently, the high-load limit of HCCI combustion is imposed by a phenomenon commonly known as ringing. Ringing results when the kinetically-driven autoignited combustion process proceeds in such a way as to form strong pressure waves which reverberate in the engine. Inhomogeneities and gradients in mixture reactivity lead certain regions to react ahead of others, and as a result, coupling can occur between a pressure wave and the reaction front. This paper seeks first to sort several related but distinct issues that impose the high load limit: ringing, engine damage, peak in-cylinder pressure, peak rate of pressure rise, and engine noise. The fundamental gasdynamics underlying the upper load limit for premixed, autoignited engines are explored and elucidated with a quasi-1D reacting compressible flow model. This model is then used to interpret published engine data in which the autoignition of premixed, stoichiometric non-dilute methane and air at 60:1 compression ratio is studied, both with and without ringing. Finally, based on the understanding gained, the model is used to propose a strategy for achieving high load, naturally aspirated, stoichiometric HCCI.