Zipf’s law has long been used to explain urban hierarchies, suggesting that city sizes follow a predictable power-law distribution. While widely applied across spatial and historical contexts, its effectiveness is debated—particularly in representing the “fat tail” of the distribution, which includes smaller urban centers. This study proposes a more accurate alternative: a sigmoid-based distribution function. Unlike Zipf’s law, the sigmoid function captures the full spectrum of urban hierarchies, including minor cities, with greater precision. It also addresses limitations found in Pareto and log-normal models, which tend to focus only on large cities or require hybrid approaches. When tested on all European countries, the sigmoid function consistently demonstrated strong applicability, suggesting it may offer a more robust framework for analyzing urban systems. This approach could reshape how researchers model city size distributions and understand spatial organization across regions.