A new approach is used for the determination of the theoretical distribution of low flows in a highly developed basin. As estimates of water diversions and return flows from irrigation may have high errors, difficulties arise in transforming an observed series of river flows to a natural series, which is a prior requirement in a statistical analysis of this type. A priori reasoning suggests that the net diversions may be represented by linear, non-linear or truncated functions of river flows. A two-component log-normal distribution is proposed, in which the first component represents the natural low flows in the basin, unaffected by irrigation, and the second component models the effects of diversions, return flows and other regulations. The adopted diversion rule provides the link between the components. The maximum likelihood method is applied for parameter estimation, but simplified procedures based on the method of moments are investigated, and one which results in a sufficiently good fit is obtained. The feasibility of relating the constants of the net diversion rules to physical parameters such as catchment area is investigated. The method is applied to the Po basin, the largest in Italy.