Standard accounts hold that regularities of behavior must be arbitrary to constitute a convention. Yet, there is growing consensus that conventionality is a graded phenomenon, and that conventions can be more or less natural. I develop an account of natural conventions that distinguishes two basic dimensions of conventional naturalness: a probabilistic dimension and an inherent one. A convention is probabilistically natural if it is likely to emerge in a population of agents, and inherently natural if its content is a regularity (...) that scores high on relevant measures for naturalness. I motivate the proposal on conceptual grounds and then showcase its descriptive benefits by discussing two case studies in language: the tendency towards word-length optimality and the prevalence of shape opacity in spoken language vocabularies. (shrink)