We consider log-growth rates of Romanian cities’ populations for all cities in the country in the period 1992-2019 on an annual basis. We construct annual, quinquennial and decennial log-growth rates and fit to them thirty-one different statistical distributions. The best results with Kolmogorov–Smirnov, Cramér–von Mises and Anderson–Darling statistics are obtained by a mixture of five stretched Gaussian distributions (5sG) with some fixed parameters, and with the AIC, BIC, HQC information criteria are obtained with mixtures of three logistic distributions (3L), that may have or may have not exponential tails. Just as an illustration, we propose a generating stochastic mechanism for the 3L. Dedicated to Laura Andrés Alcalde