Abstract The cells that continuously develop over the flame surface of an expanding spherical flame increase its area and thereby the global propagation rate, resulting in the possibility of self-acceleration. The present study examines whether this self-acceleration could be self-similar, and, if so, whether it could also be self-turbulizing. Extensive experiments at elevated pressures and thereby reduced laminar flame thicknesses and enhanced propensity to exhibit Darrieus-Landau instability were conducted for hydrogen/air mixtures over an extensive range of equivalence ratios. The results demonstrate the strong possibility of self-similar flame acceleration, weak influence of the system pressure and diffusional-thermal instability, and a corresponding moderate spread in the power-law acceleration exponent.