Collisional and frictional shape evolution of coastal and fluvial pebbles has long been at the focus of geomorphological research. Interestingly, the well-known rounded pebble shapes show remarkable similarities all around the world. The almost universal axis ratios observed in naturally occurring pebbles suggest the existence of a stable shape toward which pebbles converge during abrasion. However, no widely accepted and robust explanation for this phenomenon exists to date. The aim of the present work is to provide a novel perspective on the shape evolution of rounded pebbles. The investigation focuses on dominant motions that depend on the shape and the abrasion processes that are expected to be induced by these motions. Motivated by the big picture of shape-dependent motions of pebbles and the corresponding predicted abrasion, a highly intuitive heuristic model is constructed, in which a motion-dependent, selective curvature-driven abrasion reveals a self-exciting process that may occur during the long-term motion. Unlike previous models, the introduced approach suggests an unstable ellipsoidal shape near the axis ratios characterizing natural pebbles. In this state, changes in axis ratios are slower because of the statistical variety of expected motions, whereas for shapes that differ significantly, the self-exciting effect accelerates shape change as a dominant mode of a motion emerges. Experiments were also conducted to validate the most critical predicted behavior of the model.